Spotting pattern for placement of compounds in an array

ABSTRACT

A plurality of samples of different substances are tested for their ability to enhance or inhibit a biological process. The samples are deposited on a supporting surface, such as a ChemCard, in an array comprising at least two dots of each sample, wherein at least one of the dots of each sample is at least a predetermined distance from at least one of the dots of each of the plurality of samples. One or more assay reagents in a gel sheet, for example, are then brought in contact with the compounds and reactions with certain of the compounds are evident as the active compounds diffuse into the one or more assay reagents. The concept of having unique neighbors for each occurrence of a dot allows the definitive correlation of active compounds with the dot (and the compound) that caused the biological activity.

PRIORITY DATA

[0001] This application claims priority to U.S. Provisional PatentApplication Serial No. 60/403,729, filed Aug. 13, 2002, which isincorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to placement of compounds in anarray such that absolute identification of specific compounds thatexhibit biological activity is possible.

[0004] 2. Description of the Related Art

[0005] High Throughput Screening (HTS) is the process by which a verylarge number of substances can be simultaneously tested for biologicalreaction with an assay reagent. For example, one widely used HTStechnique utilizes 96 well test plates that are approximately 8 cm×12cm. Various compounds are placed in the wells and simultaneously testedfor biological activity as an assay reagent is placed in each of thewells.

[0006] While the use of 96 well plates greatly improves the testingefficiency of large numbers of substances, there is a need for increasedefficiency. As such, many firms in the industry are working towardsdecreasing the size of the wells on the plates so that an increasednumber of compounds may be simultaneously tested. For example, manyassays now use 384 well plates. However, as the size of the wellsfurther decreases, additional complexities are introduced in to the HTSprocess. For example, the manufacture of the wells in the plates becomesincreasingly complex and expensive. In addition, the accurate dispensingof compounds into smaller wells and other fluid handling steps becomesmore difficult and error prone.

[0007] Other researchers have increased the number of compounds on aplate by eliminating the use of wells altogether. For example, U.S. Pat.No. 5,976,813, entitled “CONTINUOUS FORMAT HIGH THROUGHPUT SCREENING,”discloses an assay format in which multiple spots of candidate materials(such as chemical compounds) are spotted onto a supporting layer,preferably in dry form, and are then transferred into a preferablyporous assay matrix, such as a gel, a filter, a fibrous material, or thelike, where an assay is performed. In the context of this type of assay,the supporting layer carrying an array of (preferably dried) assaymaterials is referred to by the name “ChemCard,” which is proprietary toDiscovery Partners International, Inc. Such usage in this disclosure issimply for purposes of convenience, and is neither an indication thatChemCard is considered generic or descriptive, nor an indication thatthe invention is limited to any particular type of ChemCard availablefrom Discovery Partners International, Inc. or similar cards from anyother vendor. The use of ChemCards carrying large numbers of driedcandidate compounds (for example), that are to be assayed for aparticular desired activity, provides a convenient, rapid, and powerfulformat for high throughput assays.

[0008] Assays of this type, which occur in a preferably porous matrix orother material in which reactants can diffuse, can sometimes produceinitially ambiguous results which will require some interpretation ortranslation to eliminate the ambiguity. Because the reactants are notheld in discrete locations, a positive result can be in the form of a“spot” that has diffused out to a diameter greater than that of theoriginal dot on the ChemCard. This spot can be of a diameter thatencompasses the corresponding locations of multiple dots.

[0009] During the course of some assays, the compound travels from theoriginal ChemCard into one or more preferably porous assay matrix layers(e.g. gel layers) or onto another surface. Although the compoundsgenerally keep their relative x, y centers, they may diffuse radially,even non-symmetrically, becoming more dilute. The eventual spot createdby the differential signal in the assay response to an “active” compound(hereafter referred to simply as “spot”) is on an image derived from amedium that is not the original ChemCard. Therefore, there can be adiscrepancy between the relative position of the center of the activespot and the relative position in which the compound was originallyplaced (hereafter referred to as the compound “dot”). Unlike assaysperformed in wells, there is not necessarily a visual outline toindicate where each compound is centered. Thus, if no errors wereintroduced in the x and y coordinates during the assay process thenidentification of each compound responsible for a spot could be made.However, error is introduced at each step of the assay process makingdefinitive identification of the compound that produced the spotincreasingly difficult. For example, error may be introduced by theliquid handler that places the compounds on the ChemCards (whetherrobotic or human), the diffusion of the compound between ChemCards, gelsand membranes, the flexibility (distortion) of gels, and the nonlinearaspects of image collection. Each of these factors contributes to anerror that is equal to the distance between the center of an imaged spotand the intended center of the compound dot on the original ChemCard,herein referred to as the dot-spot error, or DSE. The intended center ofthe compound dot on the ChemCard (the “intended location” of thecompound dot) is the location that the compound dot is to be placed onthe ChemCard, which may be different than the center of the locationthat the compound dot is actually placed on the ChemCard (e.g. the“actual location” of the compound dot). In other words, due to errorsintroduced in the process of placing the compound dot on the ChemCard,such as those introduced by the liquid handler, for example, theintended location of the dot may be different than the actual locationof the dot. In application, if the DSE is less than half of the pitch(e.g. distance) between compound dots then the active spots may beabsolutely correlated with their respective dots and a ChemCard carryingonly a single instance of each compound may allow accurateidentification of the compounds corresponding to the active spots.However, if the DSE is greater than one half the pitch between compounddots, ambiguity in the determination of the active spot is present. Assuch, a more sophisticated method of placing compounds in an array sothat the active spots may be accurately correlated with their respectivedot is desired.

SUMMARY OF THE INVENTION

[0010] In one embodiment, the present invention comprises an array of nunique materials, each of which appears in the array at least two timesand which has a plurality of neighboring materials, wherein for each ofthe n materials in the array, the neighboring materials in oneoccurrence of the material are different from the neighboring materialsof all other occurrences of the material, wherein n is greater than 25.The materials may be considered neighboring materials of a particularmaterial if they are within a predetermined radius around the particularmaterial. The predetermined radius may be in the range of about 1 mm to1 cm. The predetermined radius may be about 3mm. Alternatively, thematerials may be considered neighboring materials of a particularmaterial if they may be within a predetermined dot-pitch distance fromthe particular material. The predetermined dot-pitch distance may be 1dot pitch. The predetermined dot-pitch may be between 1 and 5 dot pitchdistances. The predetermined dot-pitch distance may be greater than 5dot pitch distances. The value of n may be greater than 300, greaterthan 4000, or greater than 9000. The array may further be combined witha planar porous assay matrix, such that a surface of the porous assaymatrix is in contact with each of the n materials of the array in such amanner that the materials can diffuse into the porous assay matrix. Theporous assay matrix may contain at least one assay reagent capable ofinteracting with any of the materials in the array that is active in atest assay, wherein the test assay displays positive results (if any)within a time period t, during which time t the materials diffuse withinthe porous assay matrix to form a spot of diameter d, and wherein“neighboring materials” may be within a predetermined distance of thecenter of the spot. The array may further comprise a second porous assaymatrix in contact with the porous assay matrix and containing at leastone assay reagent capable of interacting with any of the materials inthe array that is active in a test assay, wherein the test assaydisplays positive results (if any) within a time period t, during whichtime t the materials diffuse within the porous assay matrix and thesecond porous assay matrix to form a spot of diameter d on the secondporous assay matrix and wherein “neighboring materials” may be within apredetermined distance of the center of the spot. The “neighboringmaterials” may include materials within a radius of about 3.5 mm.

[0011] In another embodiment, any number of porous assay matrices may beused in an assay process. For example, a porous gel matrix may initiallybe applied to the ChemCard. After sufficient diffusion of the compounddots, one or more porous, or non-porous, assay matrices may betemporarily contacted with the initial porous gel matrix.

[0012] In another embodiment, the present invention includes a methodfor creating an array of a plurality of materials, each materialoccurring at least twice within the array and having differentneighboring materials in each occurrence. This method comprises (a)creating a candidate arrangement of materials containing n pairs of thematerials in a spatial relationship, (b) testing whether a firstoccurrence and a second occurrence of each of the materials havedifferent neighbors, (c) if the criteria of (b) is not satisfied,changing the spatial relationship of at least some of the n materials,and (d) repeating steps (b) and (c) until the criteria of (b) issatisfied. The candidate arrangement created in step (a) may compriseeach of the plurality of materials such that when the criteria of (b) issatisfied, the array is complete. The candidate arrangement created instep (a) may comprise a portion of the plurality of materials, themethod further comprising (e) expanding the candidate arrangement ofmaterials by increasing n by a predetermined number, and (f) repeatingsteps (b)-(e) until a final candidate arrangement is created containingeach of the plurality of materials. Changing the spatial relationship ofat least some of the n the materials may comprise determining whether aplacement of a nth material in every open location within the candidatearrangement fails to satisfy the criteria of (b), decrementing n if thenth material fails to satisfy the criteria of (b) in every open locationwithin the candidate arrangement, and changing the spatial relationshipof at least some of n the materials.

[0013] In another embodiment, a method of testing a plurality of samplesof different substances for their ability to enhance or inhibit abiological process comprises depositing in an array at least two dots ofeach of the samples onto a planar matrix such that each of the at leasttwo dots is centered at its own distinct site, wherein at least one ofthe at least two dots of each of the samples is at least a predetermineddistance from at least one of the dots of each of the plurality ofsamples, transferring the array from the planar matrix into a uniformlydispersed assay reagent, and observing the interaction of each of thesubstances with the assay reagent and correlating the interaction withan ability of each of the substances to enhance or inhibit thebiological process. The method may further comprise depositing in asecond array at least two dots of each of the samples onto a secondplanar matrix such that each of the at least two dots is centered at itsown distinct site, wherein at least one of the at least two dots of eachof the samples is at least a predetermined distance from at least one ofthe dots of each of the plurality of samples, and a pattern of placementof the dots on the second array is different than a pattern of placementof the dots on the first array, placing the uniformly dispersed assayreagent on the second planar matrix, and observing the interaction ofeach of the substances with the assay reagent and correlating theinteraction with an ability of each of the substances to enhance orinhibit the biological process. The method may further comprise placinga second uniformly dispersed assay reagent on the uniformly dispersedassay reagent, observing a second interaction of each of the substanceswith the second uniformly dispersed assay reagent, and correlating thesecond interaction with an ability of each of the substances to enhanceor inhibit the biological process. The method may further compriseplacing a third uniformly dispersed assay reagent on the seconduniformly dispersed assay reagent, observing a third interaction of eachof the substances with the third uniformly dispersed assay reagent, andcorrelating the third interaction with an ability of each of thesubstances to enhance or inhibit the biological process. The planarmatrix may comprise a plurality of alignment dots configured to diffuseinto the uniformly dispersed assay reagent, the second uniformlydispersed assay reagent, and the third uniformly dispersed assayreagent; the alignment dots on the third uniformly dispersed assayreagent providing reference points for the orientation of the thirduniformly dispersed assay reagent with respect to the planar matrix.

[0014] In another embodiment, a method of testing a plurality of samplesof different substances for their ability to enhance or inhibit abiological process comprises depositing in an array at least one dot ofeach of the samples onto a plurality of planar matrixes such that eachof the at least one dot is centered at its own distinct site, wherein atleast one of the dots of each of the samples is at least a predetermineddistance from at least one of the dots of each of the plurality ofsamples, transferring the array of samples from the plurality of planarmatrixes into a uniformly dispersed assay reagent, and observing theinteraction of each of the substances with the assay reagent andcorrelating the interaction with an ability of each of the substances toenhance or inhibit the biological process.

[0015] In another embodiment, a system for testing the interaction of aplurality of samples of different compounds with an assay reagentcomprises a relatively flat carrier configured to support the pluralityof samples and a dispensing mechanism configured to dispense at leasttwo dots of each of the plurality of samples of different compounds onthe flat carrier such that each of the at least two dots of each of theplurality of samples has a different set of neighboring compounds withina predetermined distance. The system may further comprise a detectionmechanism configured to detect interactions between each of theplurality of samples dispensed on the flat carrier and the assayreagent. The dispensing mechanism, may simultaneously dispense a portionof the plurality of samples, where the pipettes in the dispensemechanism are arranged in a particular relative orientation, on at leasttwo locations on the flat container. None of the samples in the portionof the plurality of samples may be neighboring compounds. The portion ofthe plurality of samples may comprise twelve samples. The assay reagentmay be uniformly dispersed in a gel sheet. The flat carrier may comprisea plurality of alignment dots configured to diffuse into the assayreagent and provide reference points for the orientation of the gelsheet with respect to the flat carrier.

[0016] Another embodiment comprises an array of samples in which eachsample appears at least twice and there may be at least 768 dispenses ofgroups of 12 samples.

[0017] Another embodiment comprises an array of samples in which eachsample appears at least twice and there may be at least 4608 samples,wherein the array comprises 144 columns and 64 rows and the samples maybe arranged substantially according to the relative coordinates shown inTable 1.

[0018] In another embodiment, a method for performing an assay comprisesproviding a substantially planar substrate having an array of at leasttwo dots of each of a plurality of test materials, wherein each of thedots has a plurality of neighboring test materials and is placed suchthat the neighboring materials in one occurrence of the material aredifferent from the neighboring materials of all other occurrences of thematerial, and transferring the array of test materials into auniformly-dispersed assay reagent that participates in indicating whichof the test materials may be active in the assay while maintaining therelative positioning of the test materials vis-a-vis each other.Transferring the array of test materials may comprise contacting thearray with the assay reagent and allowing the materials to diffuse intothe assay reagent. Transferring the array may comprise transferring thematerials into a first matrix, and then contacting the first matrix withthe assay reagent. Transferring the array may comprise contacting thearray with a gel into which the materials can diffuse.

[0019] These and other objects and features of the present inventionwill become more fully apparent from the following description andappended claims taken in conjunction with the following drawings, wherelike reference numbers indicate identical or functionally similarelements.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020]FIG. 1 is a perspective view of a ChemCard and a gel sheet.

[0021]FIG. 2 is a perspective view of a gel sheet placed on a ChemCard.

[0022]FIG. 3 is a top view of an image of spots transposed on a ChemCardhaving a plurality of compound dots placed thereon.

[0023]FIG. 4 is a flow chart illustrating a method of placing pairs ofcompounds in an array so that the active dot may be accuratelycorrelating with a resultant active spot.

[0024]FIG. 5 is a flow chart illustrating one method of performing block440 of FIG. 4.

[0025]FIG. 6a, 6 b, and 6 c are diagrams representing a portion of anexemplary process of placing compounds in an array so that eachoccurrence of a particular compound has different neighbors.

[0026]FIG. 7 is a flow chart illustrating a method of determining anarray S_(A) such that each of the compounds in each of the A dispensepositions satisfy the neighbor constraints.

[0027]FIG. 8 is a flowchart illustrating one method of performing theneighbor constraint checks for an exemplary compound M.

[0028]FIG. 9 illustrates a portion of a placement array geographicallyarranged as the compounds would be placed on a ChemCard.

DETAILED DESCRIPTION

[0029] In the following description, reference is made to theaccompanying drawings, which form a part hereof, and which show, by wayof illustration, specific examples or processes in which the inventionmay be practiced. Where possible, the same reference numbers are usedthroughout the drawings to refer to the same or like components. In someinstances, numerous specific details are set forth in order to provide athorough understanding of the invention. The invention, however, may bepracticed without the specific details or with certain alternativeequivalent devices and/or components and methods to those describedherein. In other instances, well-known methods and devices and/orcomponents have not been described in detail so as not to unnecessarilyobscure aspects of the invention.

[0030] In one embodiment, two compound dots are microarrayed for eachcompound to be tested in order to create a pair of active spots for eachactive compound. For each compound, the two dots are placed in positionson the same ChemCard such that each has a different set of neighborswithin a known distance (a “neighbor distance”) that is greater than theDSE. Similarly, “neighbors” of a particular compound, as used herein, isdefined as those compound within a “neighbor distance” of the center ofthe particular compound dot. In an advantageous embodiment, the neighbordistance is maximized by an algorithm such that the distance between onepair of every combination of compounds is maximized. In order to allowpositive identification of the dot corresponding to an active spot theneighbor distance should be greater than the determined DSE(representative of the errors introduced in the assay process). Invarious embodiments, the neighbor distance may vary depending on thecomplexity of an assay process. For example, in a simple assay process,with a corresponding low DSE, the algorithm may quickly provide apattern for placing the compound pairs on the ChemCard (e.g. theneighbor distance may be only slightly larger than the DSE). Likewise,in a multi-step assay, or otherwise error prone assay process, the DSEmay be much larger and require an increasingly complex algorithm, ormultiple iterations of an algorithm, in order to provide a pattern forplacing the compound pairs on the ChemCard with a neighbor distance thatis greater than the DSE. Thus, no compounds within the DSE of aparticular dot will be within the DSE of the particular dot'scounterpart dot. This concept of having unique neighbors for eachoccurrence of a dot allows the correlation of active spots with the dots(and the compounds) that caused the biological activity. While a systemand method for placing pairs of compounds on a ChemCard is described indetail herein, one of skill in the art will recognize that the conceptsdescribed herein may be applied when additional occurrences of eachcompound are used. For example, in an embodiment that places fouroccurrences of each compound on a single ChemCard, the systems andmethods described herein may be applied to ensure that each of the fouroccurrences of a specific compound have unique neighbors. In addition,one of skill in the art will recognize that a plurality of patterns thatproduce unique neighbors for each occurrence of a particular compounddot may be determined.

[0031] In one embodiment, ChemCards having the same or similardimensions as typical welled microplates used for HTS are used in orderto allow the use of existing detectors and plate handlers.

[0032]FIG. 1 is a perspective view of a ChemCard 110 and a preferablyporous assay matrix (e.g. a gel sheet 120). Throughout this descriptionthe term gel and gel sheet are used as one example of a porous assaymatrix layer. It is contemplated that any other porous assay matrixlayer may be used in place of any gel or gel sheet described herein, anda reference to a gel in this detailed description does not exclude thesubstitution of other types of assay matrices, which substitution isexpressly contemplated. For example, a non-porous matrix, such as anon-porous hydrophilic sheet, may be used to carry reagents. Thesereagents may be attached, such as by a covalent bond, for example, ormay be free to diffuse from the surface of the porous or non-poroussheet. A plurality of compound dots 130 are placed on a top surface 112of the ChemCard 110 in an array. In one embodiment, rows and columns ofdots 130 are placed on the ChemCard 110 in a honeycomb pattern, ratherthan a square array, to maximize the number of the compounds that may beplaced on the ChemCard 110. In the illustration of FIG. 1, only aportion of the dots 130 are shown on the ChemCard 110. In operation,some or substantially all of the surface 112 of the ChemCard 110 mayhave dots 130 placed thereon. In one embodiment, dots 130 are not placedon certain portions of the ChemCard 110 in order to allow the placementof alignment dots (discussed below with reference to FIG. 3). Inaddition, dots 130 may not be placed on designated regions of theChemCard so that the regions can be used for positive or negative assaycontrols.

[0033] In an advantageous embodiment, the top surface 112 of theChemCard 110 is flat in order to allow the gel sheet 120 to come incomplete contact with the compound dots 130 on the ChemCard. The directand complete contact of each of the compound dots 130 is necessary fordissolution and transfer of the compounds from the top surface 112 intothe gel sheet 120.

[0034] In one embodiment, the gel sheet 120 comprises a uniformlydispersed assay reagent in a substrate. The composition and method ofmanufacturing the gel sheet 120 is described in more detail in theco-pending application titled, “SYSTEMS AND METHODS FOR CASTING ANDHANDLING ASSAY MATRICES,” application Ser. No. 10/219081, which ishereby incorporated by reference for all purposes.

[0035] In operation, after the compound dots 130 are placed on theChemCard 110, the gel sheet 120 may be placed in direct contact with theChemCard 110, or in direct contact with a medium into which the compounddots 130 have been transferred in registry from the ChemCard 110. Assuch, each of the compounds in the dots 130 is in direct contact withthe assay reagent in the gel sheet 120. Those particular compounds thatbiologically react with the assay reagent in the gel sheet 120 typicallydiffuse, directly or indirectly, into the gel sheet 120 and create anidentifiable diffusion spot on the gel sheet. In addition, cards or gelsheets comprising other assay reagents may be applied to the gel sheet120 with the diffusion spots. In this way, a multi step assay may beperformed on a set of compound dots 130 on a single ChemCard 110.However, as the number of steps in the assay process increases (e.g.additional assay reagents in gel sheets are applied), the correlation ofthe eventual active spots with the original dots becomes increasinglydifficult.

[0036] In one embodiment, the compounds are transferred to the ChemCard110 as solutions of compound in a solvent, such as dimethyl sulfoxide(DMSO). The amount of compound in each dot is determined based on theknown concentration at which assays are typically run and the thicknessof the gel sheet or sheets 120. In an advantageous embodiment, each ofthe dots comprises about 20 ng of compound. However, the amount ofcompound varies with the particular ChemCard and its intended assaysystem, and may be any suitable value.

[0037] The minimum volume of the DMSO solution may be determined by themaximum concentration of the compound that will dissolve in the DMSOsolvent. If the concentration of a compound is too high, precipitationof the compound may occur. On the other hand, if the concentration of acompound is too low (and the volume of solution is not increased), theinteraction between the compound and the assay reagent in the gel sheetmay not be identifiable. In an advantageous embodiment, theconcentration of compound in DMSO solvent is about 1 mg/mL. Thus, ifeach dot comprises about 20 ng of compound, the volume of the DMSOsolution placed on the ChemCard in forming each dot 130 is about 20 nL(i.e. 20 ng/1 mg/mL=20 nL). In laboratory tests, 20 nL dots of solutionoccupy a diameter of less than about 1 mm, and typically fall within therange from about 0.6 to 0.7 mm. In addition, the radius of the dots 130depends on the contact angle between the DMSO solution and the surfaceof the ChemCard, such that as the contact angle decreases, the dot 130radius increases. One of skill in the art will recognize that dots ofdifferent sizes, having different concentrations of compounds, and usingdifferent solvents, may work equally as well in the present system. Theplacement of the compound dots 130 on the ChemCard 110 may also beperformed in other manners, other than by creating a solution.

[0038] In one advantageous embodiment, the number of compound dots 130on a single ChemCard 110 is 9216. Thus, if compounds are placed induplicate on the ChemCard 110, 4608 different compound dot 130 pairs maybe placed on each ChemCard.

[0039] The compounds awaiting placement on the ChemCard are typicallystored in and robotically transferred from standard microwell plates, ormicroplates. In a system using 4608 pairs of compounds per ChemCard 110,multiples of standard sized microplates may be used to supply thecompound solutions for spotting. For example, forty eight 96 wellmicroplates, twelve 384 well microplates, or three 1,536 wellmicroplates may store the necessary 4608 compounds. In addition, theefficiency of using a ChemCard carrying 9,216 compound dots may beimproved by using a number of rows and columns that are multiples ofstandard microplate rows and columns. For example, in one embodiment,the ChemCard comprises 64 rows and 144 columns such that a number ofstandard microplate rows and columns may be used to fill the 64 rows and144 columns. For example, the 64 rows may be evenly divided and filledby microplates with 8, 16, or 32 rows. Likewise, the 144 columns may beevenly divided and filled by microplates with 12, 24, or 48 columns.

[0040] In one embodiment, a dispensing mechanism dispenses a pluralityof compounds simultaneously on the ChemCard 110. For example, thedispensing mechanism may comprise a plurality of pipettes fordistribution of the compounds. The number of pipettes may vary greatlydepending on the particular objectives of the dispensing (microarraying)process, and typically range from 1 to 96 pipettes. In one embodiment,the position of each of the plurality of pipettes are at fixed locationsrelative to one another, such that all of the plurality of pipettes movein parallel. In another embodiment, each of the pipettes movesindependent of the others. In one embodiment, the range of movement ofeach pipette is exclusive, such that only a single pipette may dispenseat each location on the ChemCard 110. The number of parallel pipettesused in a particular microarraying system may largely affect theneighbor distance that may be obtained. Specifically, in a system usinga 96 pipette dispensing mechanism, the number of possible dispenselocations on a ChemCard is less than the number of possible dispenselocations a 12 pipette dispensing mechanism would have on the sameChemCard. Thus, the number of pipettes in the dispensing mechanism isdirectly related to the maximum neighbor distance that may be obtained.

[0041] In a typical compound dispensing system, each of the pipettes inthe dispensing mechanism aspirates a compound from a microwell in amicroplate, the dispensing mechanism is positioned over a predeterminedlocation of the ChemCard, and the pipettes dispense the compound in apredetermined location. The pipettes may store enough of each compoundso that multiple dispenses of the compound may occur without refillingthe pipette from the microplate. Before loading the pipettes withdifferent compounds, the pipettes should be thoroughly washed in orderto ensure that each of the compounds placed by the pipettes are pure.The washing process typically requires a significant amount of time toperform. For example, in certain embodiment, the washing processrequires more time to perform than the process of loading and aspiratingeach of the pipettes.

[0042] In one embodiment, all of the pipettes in a particular dispensingmechanism dispenses simultaneously. For example, in a 12 pipettedispensing mechanism, each of the pipettes may dispense (fire)simultaneously, depositing compounds from each of the 12 pipettes on theChemCard. Likewise, a 96 pipette dispensing mechanism may simultaneouslydispense each of the compounds in the 96 pipettes. In anotherembodiment, only a selected portion of the pipettes may besimultaneously dispensed. For example, in a system comprising a 96pipette dispensing mechanism, the dispensing mechanism maysimultaneously dispense only 12 of the 96 total pipettes. The 96 pipettedispensing mechanism may then move to another location over the ChemCardand dispense another 12 pipettes. In this particular example, theprocess may be repeated 8 times, aspirating 12 pipettes at eachlocation, in order to dispense each of the 96 pipettes. Thus, thedispensing mechanism may dispense 8 different sets of 12 compounds, atmultiple locations, without washing the pipettes. By reducing the numberof wash cycles required (by having more pipettes operate in parallel,for example) to place a specific number of compounds on a ChemCard thetime required to place the compounds on a ChemCard may be reduced. Inaddition, the dispensing of only a portion of the total pipettes in adispense mechanism may allow a larger neighbor distance in the array.For example, if only 12 pipettes of a 96 pipette dispensing mechanismare dispensed at each location above the ChemCard, the neighbor distancemay be equivalent to the neighbor distance in a system using asimultaneous aspirating 12 pipette dispensing mechanism.

[0043] If the dispensing mechanism simultaneously fires more than onepipette, the pitch between the pipettes may well need to be greater thanthe predetermined distance between neighbors for the particular assayprocess. Otherwise, each occurrence of the compound in a particulardispensing mechanism would have the same neighbors. In one exemplaryembodiment, the dispensing mechanism comprises 12 pipettes, such that 12compounds are simultaneously picked up from a microplate andsimultaneously dispensed on the ChemCard. Each set of 12 compounds isdispensed on at least two different locations on the ChemCard beforewashing the pipettes and retrieving the next 12 compounds for placement.Subsequent dispenses of different compounds may be placed in the areasbetween the compounds placed previously. As such, compounds fromdifferent groups of dispenses may be neighbors, e.g. within a neighbordistance of one another. In one embodiment, an ink-jet type dispensingmechanism may be used to print the desired dots on the ChemCard 110. Inanother embodiment, a pin spotter may be used to apply the desired dotsto the ChemCard 110.

[0044]FIG. 2 is a perspective view of a gel sheet 120 placed on aChemCard 110. As discussed above, the ChemCard 110 includes a pluralityof compound dots to be assayed for a particular biological activity. Forexample, in one embodiment, the ChemCard 110 is covered with 9216 dotscomprising pairs of 4608 different compounds. The dots can betransferred directly or indirectly into a substrate (such as a gel) inwhich assay results are read. As the compounds diffuse into the gelsheet 120, those compounds that biologically react with the assayreagent(s) in the gel sheet 120 form detectable spots 210. The spots 210may then be identified by a detection mechanism, such as a human or(preferably) machine vision system which determines the dots 130 on theChemCard 110 that produced the spots 210 (the “active dots”). However,as indicated in FIG. 2, the size of the spots 210 on the gel sheet 120is substantially larger than the size of the dots 130 on the ChemCard(FIG. 1). As such, the definitive identification of the active dotsbecomes increasingly complex. Furthermore, during the course of an assaythe compound may travel from the original ChemCard 110 into multiple gellayers 120 or onto other surfaces. In fact, the compounds may betransferred to any number of gel layers 120 in an assay process and anynumber of gel layers 120 carrying reagents may be applied to layerscarrying the compounds. Also, any number of non-porous surfaces carryingreagents may be applied to a gel layer 120 in the assay process. Theattachment of reagents to a non-porous surfaces, such as a solidsurface, may be accomplished by dipping, or otherwise covering, thesurface of the non-porous surface with a reagent solution.Alternatively, reagents may be attached to a non-porous surfacechemically (such as by a covalent bond). Thus, the eventual spot 210created by the differential signal in the assay response to an activecompound dot 130 a ( active dots 130 a are those dots 130 thatcorrespond to an active spot 210) is on a medium that is not theoriginal ChemCard 110. Therefore, the identification of the absolutecenter of the spots 210 may not accurately identify the active dot 130 aas there may be a discrepancy between the relative position of thecenter of the active spot 210 and the intended center of the compounddot 130 (FIG. 1) on the ChemCard 110.

[0045]FIG. 3 is a top view of an image of spots (e.g. a photo of thefinal gel layer 120 used in the assay process) transposed on a ChemCard110 having a plurality of compound dots 130 placed thereon. The image ofspots 210 a, 210 b, and 210 c may be captured from the most recentlyapplied gel layer 120 in a multiple step assay process. For example, afirst gel layer 120 may be placed on the ChemCard 110. The first gellayer 120 may have a first assay, or alternatively, may not have anyassay reagents. The first gel layer 120 may be removed from the ChemCard110 and placed on a second gel layer 120 (having different assayreagents than the first gel layer 120). The first and second gel layersmay then be separated and a third gel layer placed in contact with thesecond gel layer. The image of spots 210 on the third gel layer may thenbe captured. The spots 210 are thus representative of the biologicalreactions between the compounds from dots 130 through the first gellayer, the second gel layer, and the third gel layer. It should beunderstood that in some instances, the actual compound may not itself bepresent in the spot that is imaged, but instead, the compound has actedas a catalyst or trigger for the creation of an imageable spot fromother reagents.

[0046] Throughout each stage of the above described multiple stage assayprocess, a degree of error is introduced in the absolute locations ofthe spots 210 with respect to the intended and actual locations of theircorresponding dots 130 on the ChemCard (e.g. cumulatively the DSE). Assuch, the center of the active dot 130 a (e.g. the actual location)associated with each of the spots 210 may not lie in the absolute centerof the spot 210. For example, in FIG. 3, the active dot 130 a reactswith each of the gel layers in the assay process to create active spot210 a. However, through the errors introduced in the various steps ofthe assay process, the center of the active dot 130 a is not in theabsolute center of the spot 210 a. As such, the identification of activedots (e.g. dot 130 a) may not be positively identified by comparing thelocations of the image including spots 210 to the original dot 130locations on the ChemCard.

[0047] In one embodiment, alignment dots 320 are placed on the peripheryof the ChemCard in order to ensure that the orientation and alignment ofthe final image containing spots 210 may be correlated with the originalplacement of the compound dots 130 for determination of the active dots130 a. In the embodiment of FIG. 3, the twenty-two alignment dotsprovide an asymmetric pattern in both mirror planes, even with theabsence, obscuration, or addition of some spots developing in thealignment dot region. This asymmetry is desirable since during the assayprocess porous assay matrixes (such as gel sheets), membranes, andimages can be flipped relative to the original ChemCard. In oneembodiment, the alignment dots 320 are outside of the array where thecompounds are placed to reduce interference with the assay of thecompounds and, conversely, to reduce the effect of active spots on thealignment dots 320, as well as to make dot dispensing more efficient.The placement of the alignment dots outside the array of compounds mayalso advantageously increase the neighbor distance by providing a largerarea for a multi-pipette dispensing mechanism to simultaneously dispensemultiple compounds. In contrast, if the alignment dots are place in themiddle of the array of compounds, the possible dispense locations for asimultaneous multi-pipette dispense is decreased.

[0048]FIG. 4 is a flow chart illustrating a method of placing pairs ofcompounds in an array so that the active dot 130 a may be accuratelycorrelating with a resultant, active spot 210. FIG. 4 illustrates theconcept of placing the pairs of compounds in an array such that eachoccurrence of a particular compound has different neighbors. Theneighbor distance should be selected to include at least all of thecompounds within the DSE for the particular assay. Accordingly, becausethe DSE depends on several aspects of the assay process, the number ofneighbors for each compound may vary greatly depending on the particularassay method being used. In one embodiment, neighbors of a particularcompound dot 130 include all dots 130 within a 3 mm radius. In otherembodiments, the neighbors of a particular compound dot may includethose dots within a smaller radius, e.g. 1 mm, 1.5 mm, 2 mm, or a largerradius, e.g. 4 mm, 6 mm, 1 cm. Those of skill in the art will recognizethat the techniques disclosed herein are equally applicable to each ofthe above examples. Alternatively, the neighbors can include all thosecompounds within a given dot-pitch distance, such as those within aradius of 1 dot pitch, or 1.5, 2, 3, 4, 5, 8, or 10 dot pitch distances.Likewise, the neighbors may include an absolute number of neighboringdots. For example, in a system using a honeycomb pattern dot placement,the number of neighbors for any particular dot (excluding those dots onthe edges of the card) may include the 6 immediately adjacent neighbors.In like manner, in a system using a honeycomb pattern dot placement, thenumber of neighbors may include two rings of surrounding dots, or 18dots. One of skill in the art will recognize that an absolute number ofneighboring dots may be extended to include any desired number ofsurrounding dots. Furthermore, in a system using any other pattern fordot placement (such as a grid pattern, for example) each of the abovedescribed methods for determining neighbors is equally applicable.

[0049] In block 410, a candidate array of pairs of n compounds iscreated. As mentioned above, in one embodiment, 4608 different compoundsare placed on the ChemCard 110. Thus, in an embodiment using pairs ofeach compound, a total of 9216 dots will be placed on the ChemCard 110.In one embodiment, the candidate array comprises a matrix of X rows andY columns, where X * Y=the total number of dots (e.g. 9216), where eachcoordinate of the assay contains a representation of one of thecompounds (e.g. numbers 1-4608). As such, the array would contain twooccurrences of each number 1-4608. In one embodiment, the candidatearray begins with n=1, such that only a single pair of compounds arepositioned in the array. However, it is contemplated that any number ofcompounds may be positioned in the array in block 410. In fact, in oneembodiment all of the compounds that are to be placed in the array areassigned a random location in the array in block 410 such that the arrayis initially filled with two complete sets of the numbers from 1-4608.

[0050] In block 420, the neighbors of each occurrence of a compound aredetermined. In one embodiment, the neighbors of a particular compoundinclude a predetermined number of compounds surrounding the particularcompound in the X and Y directions in the candidate array. In anotherembodiment, neighbors of a particular compound include those compoundswithin a predetermined radius of the particular compound.

[0051] In decision block 430, the method determines whether a firstoccurrence and second occurrence of each compound have differentneighbors (i.e. exclusively unique neighbors). This process is referredto herein as a constraint check, wherein the constraints are satisfiedwhen the first occurrence and second occurrence of a compound pair havenone of the same neighbors. For example, each occurrence of a particularcompound may have 40 neighbors. Block 430 determines whether any of the40 neighbors to the first occurrence are the same as any of the 40neighbors to the second occurrence. If decision block 430 determinesthat there are occurrences of compounds in the array that have the sameneighbors, the candidate array is changed in block 440. If the candidatearray including pairs of compounds having the same neighbors is used inthe assay process the active spots will not be definitively matched to acompound dot on the ChemCard.

[0052] In block 440, the spatial relationship (e.g. coordinates in thecandidate array) of at least some of the materials in the array arechanged. Many different methods of changing the spatial relationship ofthe array are possible in this block 440. For example, in oneembodiment, the entire candidate array may be refilled in random order.In another embodiment, the locations of those pairs of compounds thatare both neighbors to a particular compound may be changed. For example,if 100 pairs (200 dots) of neighbors are common to pairs of compounds,the locations of the 200 dots may be adjusted at random, shifted, oradjusted by an algorithm, leaving the remaining dots in their respectivepositions. In another embodiment, a genetic algorithm may be implementedto adjust the spatial arrangement of the compounds in the candidatearray. See the discussion with reference to FIG. 5 for further detail onchanging the spatial relationship of dots in the candidate array.

[0053] After the spatial relationship of the compounds in the candidatearray has been adjusted (block 440), the method returns to block 420which determines the neighbors of each occurrence of the compounds, andto block 430 which repeats the constraint check on the changed candidatearray. The process of blocks 420, 430 and 440 continues until every pairof compounds passes the constraint check of block 430.

[0054] After the constraints of block 430 have been satisfied, block 450determines whether all compounds that are to be placed in the candidatearray have already been placed in the array. For example, in anembodiment using 4,608 different compounds, when n=4,608 all of thecompounds have been placed in the array. Thus, in block 430, while n isless than the total number of compounds to be placed in the array (4,608in one exemplary embodiment), the method moves to block 460. On theother hand, if all compounds have been placed in the array (e.g. n=thetotal number of compounds to be placed in the array), the method movesto block 470. Thus, in an embodiment that places all compounds in thecandidate array prior to performing any constraint check (e.g. allcompounds are placed in block 410), blocks 450 and 460 are not necessarybecause all n pairs of materials are always placed in the candidatearray. Therefore, in such an embodiment, when the constraint check ofblock 430 is satisfied, the method continues directly to block 470.

[0055] In block 460, the candidate array is expanded by incrementing n,i.e. the number of pairs of compounds in the array. In one embodiment,the position of the additional compound pair(s) may be determined atrandom. In another embodiment, the additional compound pair(s) may beinserted in to those remaining locations in the candidate array that arefurthest away from one another.

[0056] In block 470, the candidate array becomes the final array thatwill be used for placement of the compound dots 130 on the ChemCard 110(See FIGS. 1 and 3, for example).

[0057]FIG. 5 is a flow chart illustrating one method of performing block440 of FIG. 4. When the process of FIG. 5 is implemented in theplacement method of FIG. 4, the position of the compound pair that wasmost recently added to the candidate array is changed if there is aconstraint violation in block 430. If the position of the compound pairthat was most recently added to the candidate array cannot be changed toconform to satisfy the constraints in block 430, the position of thepreviously added compound pair (e.g. n−1) will be adjusted and locationof acceptable positions for the most recently added pair of compounds(e.g. n) will again be attempted.

[0058] In decision block 510, if all possible locations in the candidatearray for the nth pair of compounds, e.g. the most recently added pairof compounds, have been unsuccessfully tested against the constraintsrequirements of block 430, then block 530 decrements the value of n.Thus, block 530 performs a step back (or more than one step back) in theaddition of new pairs of compounds to the candidate array in order towork around a constraint violation that could not be avoided throughmovement of the most recently added pair of compounds.

[0059] In block 520, the position of at least one of the nth pair ofcompounds in the candidate array is changed. If n has just beendecremented in block 530, the nth pair of compounds has previouslysatisfied the constraints of block 430. However, the position of the nthpair in the candidate array is adjusted to another location thatsatisfies the constraints of block 430 in an attempt to change thespatial arrangement so that the now n+1 pair of compounds (i.e. the pairthat failed the constraints test for every location in block 510) may bemoved to a location that satisfies the constraints of block 430. One ofskill in the art will recognize that the step back function of block 530may step back multiple levels in the placement of compound pairs (e.g. nmay be decremented multiple times) in order to change the spatialarrangement of the candidate array so that the previously constraintviolating pair of compounds may satisfy the constraints of block 430.

[0060] After block 520 has changed the position of at least one of thenth pair of compounds, the method returns to block 420 which determinesthe neighbors of each occurrence of compounds, and to block 430 whichperforms the constraint check. The process of blocks 520, 420, 430, and510 will continue until either (a) a position for the nth pair ofcompounds in the candidate arrangement that satisfies the constraints ofblock 430 is identified or (b) n is decremented by block 530 as a resultof the inability to satisfy the constraints of block 430 by adjustingthe position of the nth pair of compounds.

[0061]FIG. 6a, 6 b, and 6 c are diagrams representing a portion of anexemplary process of placing compounds in an array so that eachoccurrence of a particular compound has different neighbors. FIG. 6aillustrates the position of compound pairs represented by the letters A,B, C, D, E, F, G, H, and I, in a portion of an array. As shown in FIG.6, two occurrences of each compound are positioned in the array. Forexample, compound A is placed at locations 610 and 612. FIG. 6a alsoillustrates the range of neighbors that will be considered forconstraints checks. In particular, the range of neighbors in FIG. 6covers a radius of approximately 1.5 times the pitch of the compounds.However, as discussed above, the neighbor distance may vary depending onthe particular assay process. For example, in one embodiment withcompound dots placed in a honeycomb pattern on the ChemCard with avertical pitch of about 1.125 mm, a horizontal pitch of about 1.5 mm,and a diagonal pitch of about 0.95 mm, an algorithm has determined anarray of 4608 compound pairs that have unique neighbors within aneighbor distance of about 3.5 mm. Alternatively, the range of neighborsmay include a certain number of surrounding compounds in each directionrather than being limited by an absolute distance.

[0062] In FIG. 6a, the range of neighbors for the occurrences ofcompound A at location 610 and 612 are indicated by circles 610 n and612 n, respectively. Thus, neighbors of the occurrence of compound A atlocation 610 include compound G and neighbors of the occurrence ofcompound A at location 612 include compound I. Because each of theoccurrences of compound A (i.e. at location 610 and 612) have differentneighbors, the position of the pair of compound A dots satisfies theconstraints, as described with reference to block 430 of FIG. 5.

[0063]FIG. 6b illustrates the position of compound pairs represented bythe letters A-I and, additionally, a candidate placement of compound J.As indicated in FIG. 6b, the pair of compound J dots are preliminarilyplaced at locations 620 and 622 within the candidate array, and theneighbors of the two occurrences include those compounds that are atleast partially within the circles 620 n and 622 n, respectively. Inparticular, neighbors of the occurrence of compound J at location 620include compound D and neighbors of the occurrence of compound J atlocation 622 include compounds D and F. Because each of the occurrencesof compound J have a common neighbor, D, the position of the pair ofcompound J dots does not satisfy the placement constraints. If compoundJ were left in the position indicated in FIG. 6b, the reaction by eithercompound D or J in the assay process may create spots on the final gelsheet that are not definitively attributable to either compound D or J.Thus, the candidate arrangement of compounds shown in FIG. 6b should beadjusted.

[0064]FIG. 6c illustrates the position of compound pairs represented bythe letters A-J, wherein the position of compound J previously atlocation 620 (FIG. 6b) has been changed to a new location 630. Theneighbors of compound J at location 630 include compound B and theneighbors of compound J at location 622 include compounds D and F. Thus,the movement of compound J from location 620 to 630 removes theduplicate neighbors from the occurrences of compound J. As such, thecurrent candidate array satisfies the placement constraints andadditional compounds, if any, may be added using a similar process.

[0065] In one embodiment, the ChemCard comprises columns on the leftmostand rightmost areas of the field of view-that are not microarrayed witheither alignment dots or compounds. These regions are left for the blankduring the microarraying process such that they can be used for assaycontrols by the end user. There are many different HTS assays that canbe run on the same compounds, and many copies of each ChemCard can bemade for the various assays that will be run on them. Each assay canhave its own control compounds to verify and quantitate an activeresponse to the assay (positive controls). One feature of thisembodiment is that no array locations need to be sacrificed for negativecontrols, since background, defined as the lack of influence ofcompounds, exists throughout the image. In contrast, in a typicalmicroplate assay, wells must be used for negative controls.

[0066] In one embodiment, an assay process uses a robotic dispensingmechanism to place the compounds on the ChemCard. For example, in anexemplary embodiment, the dispensing mechanism comprises 12 pipettesthat dispense each compound twice on the ChemCard (creating two dots ofeach compound) so that each of the two dots has a different set ofneighboring compounds. As discussed above, the number of simultaneouspipette dispenses at each location over the ChemCard may affect both theefficiency of the microarraying process (e.g. the number of washings maybe decreased by firing only a portion of the pipettes at each location)and the neighbor distance (e.g. as the number of simultaneous pipettedispenses increases, the neighbor distance decreases).

[0067] In an assay using a ChemCard having 4608 unique compounds (andthus 9216 dots), the dispensing mechanism makes 768 (9216/12=768)dispenses on the ChemCard in order to place each of the 9216 dots. Assuch, the algorithm that determines the locations of the dots on theChemCard must allow for the dispensing of all 12 pipettes at eachlocation. Table 1 contains the relative positions of the 9216 dots, in Xand Y coordinates ranging from (0,0) to (64,144), according to oneadvantageous embodiment. Specifically, the column labeled “DOT#” assignsa number from 1-9216 to each specific dot, “REP” is either 1 or 2indicating the 1^(st) and 2^(nd) placement of a compound, “COL”identifies the horizontal position (X), and “ROW” identifies thevertical position (Y). Each pair of sequential odd and even numbers,beginning with DOT# 1, represent the two dots of a particular compound(e.g. REP 1 and REP 2). For example, DOT# 1 and 2 are the same compound,DOT# 75 and 76 are the same compound, and DOT# 4227 and 4228 are thesame compound.

[0068] The dot positions indicated in Table 1 were formulated for usewith compounds having a diameter of about 0.7 mm, a minimum dot-pitch ofabout 0.95 mm and using a neighbor distance of about 3.5 mm. As such,each of the compounds has a plurality of neighbors. The arrangement ofthe compounds in Table 1 was determined so that each occurrence of aparticular compound (two occurrences of each compound are used in thisexample) has exclusively different neighbors. The arrangement ofcompounds in Table 1 is exemplary and represents only one of a pluralityof possible patterns for compounds in a (64,144) array according to thepresent invention.

[0069] While the position of the dots shown in Table 1 was formulated sothat a dispensing mechanism comprising 12 pipettes may dispense all 12compounds at each dispensing mechanism location, one of skill in the artwill recognize the dots may be placed in other manners. For example, thedots may be placed by a single pipette that makes 9216 separatedispenses on the ChemCard (e.g. 2 dispenses of each compounds).Alternatively, the agorithm may be modified to generate a pattern thatmay be used in a system using a sing mechanism comprising any number ofpipettes, such as 2, 4, 6, 8, 10, 14, 20, 24, 96, for example.

[0070] In addition, if a particular assay process is a multi stepprocess or is otherwise more prone to errors in the locations of thedots, the range of neighbors may be expanded to include additional dots.For example, neighbors may be defined as those dots within 5 mm of oneanother. TABLE 1 DOT# REP COL ROW 1 1 37 5 2 2 73 9 3 1 115 6 4 2 4 4 51 49 5 6 2 85 9 7 1 127 6 8 2 16 4 9 1 61 5 10 2 97 9 11 1 139 6 12 2 284 13 1 73 6 14 2 1 4 15 1 11 42 16 2 120 35 17 1 85 6 18 2 13 4 19 1 2342 20 2 132 35 21 1 97 6 22 2 25 4 23 1 35 42 24 2 144 35 25 1 46 40 262 45 35 27 1 113 33 28 2 11 41 29 1 58 40 30 2 57 35 31 1 125 33 32 2 2341 33 1 70 40 34 2 69 35 35 1 137 33 36 2 35 41 37 1 11 4 38 2 6 4 39 112 10 40 2 39 40 41 1 23 4 42 2 18 4 43 1 24 10 44 2 51 40 45 1 35 4 462 30 4 47 1 36 10 48 2 63 40 49 1 1 42 50 2 117 5 51 1 79 43 52 2 47 853 1 13 42 54 2 129 5 55 1 91 43 56 2 59 8 57 1 25 42 58 2 141 5 59 1103 43 60 2 71 8 61 1 1 40 62 2 10 38 63 1 3 38 64 2 44 3 65 1 13 40 662 22 38 67 1 15 38 68 2 56 3 69 1 25 40 70 2 34 38 71 1 27 38 72 2 68 373 1 11 6 74 2 113 34 75 1 77 7 76 2 45 39 77 1 23 6 78 2 125 34 79 1 897 80 2 57 39 81 1 35 6 82 2 137 34 83 1 101 7 84 2 69 39 85 1 119 3 86 273 11 87 1 111 3 88 2 74 36 89 1 131 3 90 2 85 11 91 1 123 3 92 2 86 3693 1 143 3 94 2 97 11 95 1 135 3 96 2 98 36 97 1 37 13 98 2 73 17 99 1115 14 100 2 4 12 101 1 49 13 102 2 85 17 103 1 127 14 104 2 16 12 105 161 13 106 2 97 17 107 1 139 14 108 2 28 12 109 1 73 14 110 2 1 12 111 111 50 112 2 120 43 113 1 85 14 114 2 13 12 115 1 23 50 116 2 132 43 1171 97 14 118 2 25 12 119 1 35 50 120 2 144 43 121 1 46 48 122 2 45 43 1231 113 41 124 2 11 49 125 1 58 48 126 2 57 43 127 1 125 41 128 2 23 49129 1 70 48 130 2 69 43 131 1 137 41 132 2 35 49 133 1 11 12 134 2 6 12135 1 12 18 136 2 39 48 137 1 23 12 138 2 18 12 139 1 24 18 140 2 51 48141 1 35 12 142 2 30 12 143 1 36 18 144 2 63 48 145 1 1 50 146 2 117 13147 1 79 51 148 2 47 16 149 1 13 50 150 2 129 13 151 1 91 51 152 2 59 16153 1 25 50 154 2 141 13 155 1 103 51 156 2 71 16 157 1 1 48 158 2 10 46159 1 3 46 160 2 44 11 161 1 13 48 162 2 22 46 163 1 15 46 164 2 56 11165 1 25 48 166 2 34 46 167 1 27 46 168 2 68 11 169 1 11 14 170 2 113 42171 1 77 15 172 2 45 47 173 1 23 14 174 2 125 42 175 1 89 15 176 2 57 47177 1 35 14 178 2 137 42 179 1 101 15 180 2 69 47 181 1 119 11 182 2 7319 183 1 111 11 184 2 74 44 185 1 131 11 186 2 85 19 187 1 123 11 188 286 44 189 1 143 11 190 2 97 19 191 1 135 11 192 2 98 44 193 1 37 21 1942 73 25 195 1 115 22 196 2 4 20 197 1 49 21 198 2 85 25 199 1 127 22 2002 16 20 201 1 61 21 202 2 97 25 203 1 139 22 204 2 28 20 205 1 73 22 2062 1 20 207 1 11 58 208 2 120 51 209 1 85 22 210 2 13 20 211 1 23 58 2122 132 51 213 1 97 22 214 2 25 20 215 1 35 58 216 2 144 51 217 1 46 56218 2 45 51 219 1 113 49 220 2 11 57 221 1 58 56 222 2 57 51 223 1 12549 224 2 23 57 225 1 70 56 226 2 69 51 227 1 137 49 228 2 35 57 229 1 1120 230 2 6 20 231 1 12 26 232 2 39 56 233 1 23 20 234 2 18 20 235 1 2426 236 2 51 56 237 1 35 20 238 2 30 20 239 1 36 26 240 2 63 56 241 1 158 242 2 117 21 243 1 79 59 244 2 47 24 245 1 13 58 246 2 129 21 247 191 59 248 2 59 24 249 1 25 58 250 2 141 21 251 1 103 59 252 2 71 24 2531 1 56 254 2 10 54 255 1 3 54 256 2 44 19 257 1 13 56 258 2 22 54 259 115 54 260 2 56 19 261 1 25 56 262 2 34 54 263 1 27 54 264 2 68 19 265 111 22 266 2 113 50 267 1 77 23 268 2 45 55 269 1 23 22 270 2 125 50 2711 89 23 272 2 57 55 273 1 35 22 274 2 137 50 275 1 101 23 276 2 69 55277 1 119 19 278 2 73 27 279 1 111 19 280 2 74 52 281 1 131 19 282 2 8527 283 1 123 19 284 2 86 52 285 1 143 19 286 2 97 27 287 1 135 19 288 298 52 289 1 37 29 290 2 73 33 291 1 115 30 292 2 4 28 293 1 49 29 294 285 33 295 1 127 30 296 2 16 28 297 1 61 29 298 2 97 33 299 1 139 30 3002 28 28 301 1 73 30 302 2 1 28 303 1 11 66 304 2 120 59 305 1 85 30 3062 13 28 307 1 23 66 308 2 132 59 309 1 97 30 310 2 25 28 311 1 35 66 3122 144 59 313 1 46 64 314 2 45 59 315 1 113 57 316 2 11 65 317 1 58 64318 2 57 59 319 1 125 57 320 2 23 65 321 1 70 64 322 2 69 59 323 1 13757 324 2 35 65 325 1 11 28 326 2 6 28 327 1 12 34 328 2 39 64 329 1 2328 330 2 18 28 331 1 24 34 332 2 51 64 333 1 35 28 334 2 30 28 335 1 3634 336 2 63 64 337 1 1 66 338 2 117 29 339 1 79 67 340 2 47 32 341 1 1366 342 2 129 29 343 1 91 67 344 2 59 32 345 1 25 66 346 2 141 29 347 1103 67 348 2 71 32 349 1 1 64 350 2 10 62 351 1 3 62 352 2 44 27 353 113 64 354 2 22 62 355 1 15 62 356 2 56 27 357 1 25 64 358 2 34 62 359 127 62 360 2 68 27 361 1 11 30 362 2 113 58 363 1 77 31 364 2 45 63 365 123 30 366 2 125 58 367 1 89 31 368 2 57 63 369 1 35 30 370 2 137 58 3711 101 31 372 2 69 63 373 1 119 27 374 2 73 35 375 1 111 27 376 2 74 60377 1 131 27 378 2 85 35 379 1 123 27 380 2 86 60 381 1 143 27 382 2 9735 383 1 135 27 384 2 98 60 385 1 9 4 386 2 8 42 387 1 78 38 388 2 119 2389 1 21 4 390 2 20 42 391 1 90 38 392 2 131 2 393 1 33 4 394 2 32 42395 1 102 38 396 2 143 2 397 1 84 8 398 2 37 4 399 1 74 6 400 2 47 35401 1 96 8 402 2 49 4 403 1 86 6 404 2 59 35 405 1 108 8 406 2 61 4 4071 98 6 408 2 71 35 409 1 74 4 410 2 120 33 411 1 116 2 412 2 38 36 413 186 4 414 2 132 33 415 1 128 2 416 2 50 36 417 1 98 4 418 2 144 33 419 1140 2 420 2 62 36 421 1 5 11 422 2 9 7 423 1 7 9 424 2 43 35 425 1 17 11426 2 21 7 427 1 19 9 428 2 55 35 429 1 29 11 430 2 33 7 431 1 31 9 4322 67 35 433 1 120 36 434 2 76 41 435 1 44 8 436 2 9 38 437 1 132 36 4382 88 41 439 1 56 8 440 2 21 38 441 1 144 36 442 2 100 41 443 1 68 8 4442 33 38 445 1 76 4 446 2 81 6 447 1 40 39 448 2 117 36 449 1 88 4 450 293 6 451 1 52 39 452 2 129 36 453 1 100 4 454 2 105 6 455 1 64 39 456 2141 36 457 1 38 35 458 2 8 4 459 1 118 38 460 2 12 9 461 1 50 35 462 220 4 463 1 130 38 464 2 24 9 465 1 62 35 466 2 32 4 467 1 142 38 468 236 9 469 1 114 2 470 2 77 6 471 1 10 37 472 2 37 1 473 1 126 2 474 2 896 475 1 22 37 476 2 49 1 477 1 138 2 478 2 101 6 479 1 34 37 480 2 61 1481 1 9 12 482 2 8 50 483 1 78 46 484 2 119 10 485 1 21 12 486 2 20 50487 1 90 46 488 2 131 10 489 1 33 12 490 2 32 50 491 1 102 46 492 2 14310 493 1 84 16 494 2 37 12 495 1 74 14 496 2 47 43 497 1 96 16 498 2 4912 499 1 86 14 500 2 59 43 501 1 108 16 502 2 61 12 503 1 98 14 504 2 7143 505 1 74 12 506 2 120 41 507 1 116 10 508 2 38 44 509 1 86 12 510 2132 41 511 1 128 10 512 2 50 44 513 1 98 12 514 2 144 41 515 1 140 10516 2 62 44 517 1 5 19 518 2 9 15 519 1 7 17 520 2 43 43 521 1 17 19 5222 21 15 523 1 19 17 524 2 55 43 525 1 29 19 526 2 33 15 527 1 31 17 5282 67 43 529 1 120 44 530 2 76 49 531 1 44 16 532 2 9 46 533 1 132 44 5342 88 49 535 1 56 16 536 2 21 46 537 1 144 44 538 2 100 49 539 1 68 16540 2 33 46 541 1 76 12 542 2 81 14 543 1 40 47 544 2 117 44 545 1 88 12546 2 93 14 547 1 52 47 548 2 129 44 549 1 100 12 550 2 105 14 551 1 6447 552 2 141 44 553 1 38 43 554 2 8 12 555 1 118 46 556 2 12 17 557 1 5043 558 2 20 12 559 1 130 46 560 2 24 17 561 1 62 43 562 2 32 12 563 1142 46 564 2 36 17 565 1 114 10 566 2 77 14 567 1 10 45 568 2 37 9 569 1126 10 570 2 89 14 571 1 22 45 572 2 49 9 573 1 138 10 574 2 101 14 5751 34 45 576 2 61 9 577 1 9 20 578 2 8 58 579 1 78 54 580 2 119 18 581 121 20 582 2 20 58 583 1 90 54 584 2 131 18 585 1 33 20 586 2 32 58 587 1102 54 588 2 143 18 589 1 84 24 590 2 37 20 591 1 74 22 592 2 47 51 5931 96 24 594 2 49 20 595 1 86 22 596 2 59 51 597 1 108 24 598 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8117 1 56 7 81182 19 42 8119 1 129 35 8120 2 128 39 8121 1 68 7 8122 2 31 42 8123 1 14135 8124 2 140 39 8125 1 45 5 8126 2 8 37 8127 1 10 6 8128 2 116 37 81291 57 5 8130 2 20 37 8131 1 22 6 8132 2 128 37 8133 1 69 5 8134 2 32 378135 1 34 6 8136 2 140 37 8137 1 46 1 8138 2 44 34 8139 1 82 36 8140 245 3 8141 1 58 1 8142 2 56 34 8143 1 94 36 8144 2 57 3 8145 1 70 1 81462 68 34 8147 1 106 36 8148 2 69 3 8149 1 10 36 8150 2 80 6 8151 1 82 68152 2 81 37 8153 1 22 36 8154 2 92 6 8155 1 94 6 8156 2 93 37 8157 1 3436 8158 2 104 6 8159 1 106 6 8160 2 105 37 8161 1 44 12 8162 2 42 458163 1 80 47 8164 2 43 12 8165 1 56 12 8166 2 54 45 8167 1 92 47 8168 255 12 8169 1 68 12 8170 2 66 45 8171 1 104 47 8172 2 67 12 8173 1 79 448174 2 78 49 8175 1 45 9 8176 2 79 15 8177 1 91 44 8178 2 90 49 8179 157 9 8180 2 91 15 8181 1 103 44 8182 2 102 49 8183 1 69 9 8184 2 103 158185 1 10 18 8186 2 42 15 8187 1 84 50 8188 2 45 12 8189 1 22 18 8190 254 15 8191 1 96 50 8192 2 57 12 8193 1 34 18 8194 2 66 15 8195 1 108 508196 2 69 12 8197 1 7 18 8198 2 43 10 8199 1 115 47 8200 2 79 47 8201 119 18 8202 2 55 10 8203 1 127 47 8204 2 91 47 8205 1 31 18 8206 2 67 108207 1 139 47 8208 2 103 47 8209 1 44 15 8210 2 7 50 8211 1 117 43 82122 116 47 8213 1 56 15 8214 2 19 50 8215 1 129 43 8216 2 128 47 8217 1 6815 8218 2 31 50 8219 1 141 43 8220 2 140 47 8221 1 45 13 8222 2 8 458223 1 10 14 8224 2 116 45 8225 1 57 13 8226 2 20 45 8227 1 22 14 8228 2128 45 8229 1 69 13 8230 2 32 45 8231 1 34 14 8232 2 140 45 8233 1 46 98234 2 44 42 8235 1 82 44 8236 2 45 11 8237 1 58 9 8238 2 56 42 8239 194 44 8240 2 57 11 8241 1 70 9 8242 2 68 42 8243 1 106 44 8244 2 69 118245 1 10 44 8246 2 80 14 8247 1 82 14 8248 2 81 45 8249 1 22 44 8250 292 14 8251 1 94 14 8252 2 93 45 8253 1 34 44 8254 2 104 14 8255 1 106 148256 2 105 45 8257 1 44 20 8258 2 42 53 8259 1 80 55 8260 2 43 20 8261 156 20 8262 2 54 53 8263 1 92 55 8264 2 55 20 8265 1 68 20 8266 2 66 538267 1 104 55 8268 2 67 20 8269 1 79 52 8270 2 78 57 8271 1 45 17 8272 279 23 8273 1 91 52 8274 2 90 57 8275 1 57 17 8276 2 91 23 8277 1 103 528278 2 102 57 8279 1 69 17 8280 2 103 23 8281 1 10 26 8282 2 42 23 82831 84 58 8284 2 45 20 8285 1 22 26 8286 2 54 23 8287 1 96 58 8288 2 57 208289 1 34 26 8290 2 66 23 8291 1 108 58 8292 2 69 20 8293 1 7 26 8294 243 18 8295 1 115 55 8296 2 79 55 8297 1 19 26 8298 2 55 18 8299 1 127 558300 2 91 55 8301 1 31 26 8302 2 67 18 8303 1 139 55 8304 2 103 55 83051 44 23 8306 2 7 58 8307 1 117 51 8308 2 116 55 8309 1 56 23 8310 2 1958 8311 1 129 51 8312 2 128 55 8313 1 68 23 8314 2 31 58 8315 1 141 518316 2 140 55 8317 1 45 21 8318 2 8 53 8319 1 10 22 8320 2 116 53 8321 157 21 8322 2 20 53 8323 1 22 22 8324 2 128 53 8325 1 69 21 8326 2 32 538327 1 34 22 8328 2 140 53 8329 1 46 17 8330 2 44 50 8331 1 82 52 8332 245 19 8333 1 58 17 8334 2 56 50 8335 1 94 52 8336 2 57 19 8337 1 70 178338 2 68 50 8339 1 106 52 8340 2 69 19 8341 1 10 52 8342 2 80 22 8343 182 22 8344 2 81 53 8345 1 22 52 8346 2 92 22 8347 1 94 22 8348 2 93 538349 1 34 52 8350 2 104 22 8351 1 106 22 8352 2 105 53 8353 1 44 28 83542 42 61 8355 1 80 63 8356 2 43 28 8357 1 56 28 8358 2 54 61 8359 1 92 638360 2 55 28 8361 1 68 28 8362 2 66 61 8363 1 104 63 8364 2 67 28 8365 179 60 8366 2 78 65 8367 1 45 25 8368 2 79 31 8369 1 91 60 8370 2 90 658371 1 57 25 8372 2 91 31 8373 1 103 60 8374 2 102 65 8375 1 69 25 83762 103 31 8377 1 10 34 8378 2 42 31 8379 1 84 66 8380 2 45 28 8381 1 2234 8382 2 54 31 8383 1 96 66 8384 2 57 28 8385 1 34 34 8386 2 66 31 83871 108 66 8388 2 69 28 8389 1 7 34 8390 2 43 26 8391 1 115 63 8392 2 7963 8393 1 19 34 8394 2 55 26 8395 1 127 63 8396 2 91 63 8397 1 31 348398 2 67 26 8399 1 139 63 8400 2 103 63 8401 1 44 31 8402 2 7 66 8403 1117 59 8404 2 116 63 8405 1 56 31 8406 2 19 66 8407 1 129 59 8408 2 12863 8409 1 68 31 8410 2 31 66 8411 1 141 59 8412 2 140 63 8413 1 45 298414 2 8 61 8415 1 10 30 8416 2 116 61 8417 1 57 29 8418 2 20 61 8419 122 30 8420 2 128 61 8421 1 69 29 8422 2 32 61 8423 1 34 30 8424 2 140 618425 1 46 25 8426 2 44 58 8427 1 82 60 8428 2 45 27 8429 1 58 25 8430 256 58 8431 1 94 60 8432 2 57 27 8433 1 70 25 8434 2 68 58 8435 1 106 608436 2 69 27 8437 1 10 60 8438 2 80 30 8439 1 82 30 8440 2 81 61 8441 122 60 8442 2 92 30 8443 1 94 30 8444 2 93 61 8445 1 34 60 8446 2 104 308447 1 106 30 8448 2 105 61 8449 1 82 8 8450 2 117 3 8451 1 11 37 8452 29 10 8453 1 94 8 8454 2 129 3 8455 1 23 37 8456 2 21 10 8457 1 106 88458 2 141 3 8459 1 35 37 8460 2 33 10 8461 1 120 39 8462 2 9 39 8463 146 4 8464 2 9 11 8465 1 132 39 8466 2 21 39 8467 1 58 4 8468 2 21 118469 1 144 39 8470 2 33 39 8471 1 70 4 8472 2 33 11 8473 1 11 11 8474 281 39 8475 1 47 37 8476 2 117 40 8477 1 23 11 8478 2 93 39 8479 1 59 378480 2 129 40 8481 1 35 11 8482 2 105 39 8483 1 71 37 8484 2 141 40 84851 118 36 8486 2 81 40 8487 1 46 38 8488 2 118 33 8489 1 130 36 8490 2 9340 8491 1 58 38 8492 2 130 33 8493 1 142 36 8494 2 105 40 8495 1 70 388496 2 142 33 8497 1 47 4 8498 2 10 41 8499 1 84 39 8500 2 83 9 8501 159 4 8502 2 22 41 8503 1 96 39 8504 2 95 9 8505 1 71 4 8506 2 34 41 85071 108 39 8508 2 107 9 8509 1 11 5 8510 2 46 39 8511 1 120 3 8512 2 11938 8513 1 23 5 8514 2 58 39 8515 1 132 3 8516 2 131 38 8517 1 35 5 85182 70 39 8519 1 144 3 8520 2 143 38 8521 1 83 41 8522 2 118 40 8523 1 484 8524 2 119 6 8525 1 95 41 8526 2 130 40 8527 1 60 4 8528 2 131 6 85291 107 41 8530 2 142 40 8531 1 72 4 8532 2 143 6 8533 1 11 7 8534 2 47 348535 1 84 5 8536 2 83 42 8537 1 23 7 8538 2 59 34 8539 1 96 5 8540 2 9542 8541 1 35 7 8542 2 71 34 8543 1 108 5 8544 2 107 42 8545 1 82 16 85462 117 11 8547 1 11 45 8548 2 9 18 8549 1 94 16 8550 2 129 11 8551 1 2345 8552 2 21 18 8553 1 106 16 8554 2 141 11 8555 1 35 45 8556 2 33 188557 1 120 47 8558 2 9 47 8559 1 46 12 8560 2 9 19 8561 1 132 47 8562 221 47 8563 1 58 12 8564 2 21 19 8565 1 144 47 8566 2 33 47 8567 1 70 128568 2 33 19 8569 1 11 19 8570 2 81 47 8571 1 47 45 8572 2 117 48 8573 123 19 8574 2 93 47 8575 1 59 45 8576 2 129 48 8577 1 35 19 8578 2 105 478579 1 71 45 8580 2 141 48 8581 1 118 44 8582 2 81 48 8583 1 46 46 85842 118 41 8585 1 130 44 8586 2 93 48 8587 1 58 46 8588 2 130 41 8589 1142 44 8590 2 105 48 8591 1 70 46 8592 2 142 41 8593 1 47 12 8594 2 1049 8595 1 84 47 8596 2 83 17 8597 1 59 12 8598 2 22 49 8599 1 96 47 86002 95 17 8601 1 71 12 8602 2 34 49 8603 1 108 47 8604 2 107 17 8605 1 1113 8606 2 46 47 8607 1 120 11 8608 2 119 46 8609 1 23 13 8610 2 58 478611 1 132 11 8612 2 131 46 8613 1 35 13 8614 2 70 47 8615 1 144 11 86162 143 46 8617 1 83 49 8618 2 118 48 8619 1 48 12 8620 2 119 14 8621 1 9549 8622 2 130 48 8623 1 60 12 8624 2 131 14 8625 1 107 49 8626 2 142 488627 1 72 12 8628 2 143 14 8629 1 11 15 8630 2 47 42 8631 1 84 13 8632 283 50 8633 1 23 15 8634 2 59 42 8635 1 96 13 8636 2 95 50 8637 1 35 158638 2 71 42 8639 1 108 13 8640 2 107 50 8641 1 82 24 8642 2 117 19 86431 11 53 8644 2 9 26 8645 1 94 24 8646 2 129 19 8647 1 23 53 8648 2 21 268649 1 106 24 8650 2 141 19 8651 1 35 53 8652 2 33 26 8653 1 120 55 86542 9 55 8655 1 46 20 8656 2 9 27 8657 1 132 55 8658 2 21 55 8659 1 58 208660 2 21 27 8661 1 144 55 8662 2 33 55 8663 1 70 20 8664 2 33 27 8665 111 27 8666 2 81 55 8667 1 47 53 8668 2 117 56 8669 1 23 27 8670 2 93 558671 1 59 53 8672 2 129 56 8673 1 35 27 8674 2 105 55 8675 1 71 53 86762 141 56 8677 1 118 52 8678 2 81 56 8679 1 46 54 8680 2 118 49 8681 1130 52 8682 2 93 56 8683 1 58 54 8684 2 130 49 8685 1 142 52 8686 2 10556 8687 1 70 54 8688 2 142 49 8689 1 47 20 8690 2 10 57 8691 1 84 558692 2 83 25 8693 1 59 20 8694 2 22 57 8695 1 96 55 8696 2 95 25 8697 171 20 8698 2 34 57 8699 1 108 55 8700 2 107 25 8701 1 11 21 8702 2 46 558703 1 120 19 8704 2 119 54 8705 1 23 21 8706 2 58 55 8707 1 132 19 87082 131 54 8709 1 35 21 8710 2 70 55 8711 1 144 19 8712 2 143 54 8713 1 8357 8714 2 118 56 8715 1 48 20 8716 2 119 22 8717 1 95 57 8718 2 130 568719 1 60 20 8720 2 131 22 8721 1 107 57 8722 2 142 56 8723 1 72 20 87242 143 22 8725 1 11 23 8726 2 47 50 8727 1 84 21 8728 2 83 58 8729 1 2323 8730 2 59 50 8731 1 96 21 8732 2 95 58 8733 1 35 23 8734 2 71 50 87351 108 21 8736 2 107 58 8737 1 82 32 8738 2 117 27 8739 1 11 61 8740 2 934 8741 1 94 32 8742 2 129 27 8743 1 23 61 8744 2 21 34 8745 1 106 328746 2 141 27 8747 1 35 61 8748 2 33 34 8749 1 120 63 8750 2 9 63 8751 146 28 8752 2 9 35 8753 1 132 63 8754 2 21 63 8755 1 58 28 8756 2 21 358757 1 144 63 8758 2 33 63 8759 1 70 28 8760 2 33 35 8761 1 11 35 8762 281 63 8763 1 47 61 8764 2 117 64 8765 1 23 35 8766 2 93 63 8767 1 59 618768 2 129 64 8769 1 35 35 8770 2 105 63 8771 1 71 61 8772 2 141 64 87731 118 60 8774 2 81 64 8775 1 46 62 8776 2 118 57 8777 1 130 60 8778 2 9364 8779 1 58 62 8780 2 130 57 8781 1 142 60 8782 2 105 64 8783 1 70 628784 2 142 57 8785 1 47 28 8786 2 10 65 8787 1 84 63 8788 2 83 33 8789 159 28 8790 2 22 65 8791 1 96 63 8792 2 95 33 8793 1 71 28 8794 2 34 658795 1 108 63 8796 2 107 33 8797 1 11 29 8798 2 46 63 8799 1 120 27 88002 119 62 8801 1 23 29 8802 2 58 63 8803 1 132 27 8804 2 131 62 8805 1 3529 8806 2 70 63 8807 1 144 27 8808 2 143 62 8809 1 83 65 8810 2 118 648811 1 48 28 8812 2 119 30 8813 1 95 65 8814 2 130 64 8815 1 60 28 88162 131 30 8817 1 107 65 8818 2 142 64 8819 1 72 28 8820 2 143 30 8821 111 31 8822 2 47 58 8823 1 84 29 8824 2 83 66 8825 1 23 31 8826 2 59 588827 1 96 29 8828 2 95 66 8829 1 35 31 8830 2 71 58 8831 1 108 29 8832 2107 66 8833 1 45 40 8834 2 9 9 8835 1 118 6 8836 2 118 2 8837 1 57 408838 2 21 9 8839 1 130 6 8840 2 130 2 8841 1 69 40 8842 2 33 9 8843 1142 6 8844 2 142 2 8845 1 46 34 8846 2 45 6 8847 1 46 35 8848 2 10 398849 1 58 34 8850 2 57 6 8851 1 58 35 8852 2 22 39 8853 1 70 34 8854 269 6 8855 1 70 35 8856 2 34 39 8857 1 10 40 8858 2 81 41 8859 1 84 368860 2 10 9 8861 1 22 40 8862 2 93 41 8863 1 96 36 8864 2 22 9 8865 1 3440 8866 2 105 41 8867 1 108 36 8868 2 34 9 8869 1 83 8 8870 2 117 388871 1 119 33 8872 2 82 9 8873 1 95 8 8874 2 129 38 8875 1 131 33 8876 294 9 8877 1 107 8 8878 2 141 38 8879 1 143 33 8880 2 106 9 8881 1 11 98882 2 119 34 8883 1 84 9 8884 2 12 36 8885 1 23 9 8886 2 131 34 8887 196 9 8888 2 24 36 8889 1 35 9 8890 2 143 34 8891 1 108 9 8892 2 36 368893 1 12 8 8894 2 119 4 8895 1 48 36 8896 2 120 37 8897 1 24 8 8898 2131 4 8899 1 60 36 8900 2 132 37 8901 1 36 8 8902 2 143 4 8903 1 72 368904 2 144 37 8905 1 120 8 8906 2 119 36 8907 1 48 2 8908 2 48 7 8909 1132 8 8910 2 131 36 8911 1 60 2 8912 2 60 7 8913 1 144 8 8914 2 143 368915 1 72 2 8916 2 72 7 8917 1 84 37 8918 2 11 40 8919 1 84 10 8920 2 1243 8921 1 96 37 8922 2 23 40 8923 1 96 10 8924 2 24 43 8925 1 108 378926 2 35 40 8927 1 108 10 8928 2 36 43 8929 1 45 48 8930 2 9 17 8931 1118 14 8932 2 118 10 8933 1 57 48 8934 2 21 17 8935 1 130 14 8936 2 13010 8937 1 69 48 8938 2 33 17 8939 1 142 14 8940 2 142 10 8941 1 46 428942 2 45 14 8943 1 46 43 8944 2 10 47 8945 1 58 42 8946 2 57 14 8947 158 43 8948 2 22 47 8949 1 70 42 8950 2 69 14 8951 1 70 43 8952 2 34 478953 1 10 48 8954 2 81 49 8955 1 84 44 8956 2 10 17 8957 1 22 48 8958 293 49 8959 1 96 44 8960 2 22 17 8961 1 34 48 8962 2 105 49 8963 1 108 448964 2 34 17 8965 1 83 16 8966 2 117 46 8967 1 119 41 8968 2 82 17 89691 95 16 8970 2 129 46 8971 1 131 41 8972 2 94 17 8973 1 107 16 8974 2141 46 8975 1 143 41 8976 2 106 17 8977 1 11 17 8978 2 119 42 8979 1 8417 8980 2 12 44 8981 1 23 17 8982 2 131 42 8983 1 96 17 8984 2 24 448985 1 35 17 8986 2 143 42 8987 1 108 17 8988 2 36 44 8989 1 12 16 89902 119 12 8991 1 48 44 8992 2 120 45 8993 1 24 16 8994 2 131 12 8995 1 6044 8996 2 132 45 8997 1 36 16 8998 2 143 12 8999 1 72 44 9000 2 144 459001 1 120 16 9002 2 119 44 9003 1 48 10 9004 2 48 15 9005 1 132 16 90062 131 44 9007 1 60 10 9008 2 60 15 9009 1 144 16 9010 2 143 44 9011 1 7210 9012 2 72 15 9013 1 84 45 9014 2 11 48 9015 1 84 18 9016 2 12 51 90171 96 45 9018 2 23 48 9019 1 96 18 9020 2 24 51 9021 1 108 45 9022 2 3548 9023 1 108 18 9024 2 36 51 9025 1 45 56 9026 2 9 25 9027 1 118 229028 2 118 18 9029 1 57 56 9030 2 21 25 9031 1 130 22 9032 2 130 18 90331 69 56 9034 2 33 25 9035 1 142 22 9036 2 142 18 9037 1 46 50 9038 2 4522 9039 1 46 51 9040 2 10 55 9041 1 58 50 9042 2 57 22 9043 1 58 51 90442 22 55 9045 1 70 50 9046 2 69 22 9047 1 70 51 9048 2 34 55 9049 1 10 569050 2 81 57 9051 1 84 52 9052 2 10 25 9053 1 22 56 9054 2 93 57 9055 196 52 9056 2 22 25 9057 1 34 56 9058 2 105 57 9059 1 108 52 9060 2 34 259061 1 83 24 9062 2 117 54 9063 1 119 49 9064 2 82 25 9065 1 95 24 90662 129 54 9067 1 131 49 9068 2 94 25 9069 1 107 24 9070 2 141 54 9071 1143 49 9072 2 106 25 9073 1 11 25 9074 2 119 50 9075 1 84 25 9076 2 1252 9077 1 23 25 9078 2 131 50 9079 1 96 25 9080 2 24 52 9081 1 35 259082 2 143 50 9083 1 108 25 9084 2 36 52 9085 1 12 24 9086 2 119 20 90871 48 52 9088 2 120 53 9089 1 24 24 9090 2 131 20 9091 1 60 52 9092 2 13253 9093 1 36 24 9094 2 143 20 9095 1 72 52 9096 2 144 53 9097 1 120 249098 2 119 52 9099 1 48 18 9100 2 48 23 9101 1 132 24 9102 2 131 52 91031 60 18 9104 2 60 23 9105 1 144 24 9106 2 143 52 9107 1 72 18 9108 2 7223 9109 1 84 53 9110 2 11 56 9111 1 84 26 9112 2 12 59 9113 1 96 53 91142 23 56 9115 1 96 26 9116 2 24 59 9117 1 108 53 9118 2 35 56 9119 1 10826 9120 2 36 59 9121 1 45 64 9122 2 9 33 9123 1 118 30 9124 2 118 269125 1 57 64 9126 2 21 33 9127 1 130 30 9128 2 130 26 9129 1 69 64 91302 33 33 9131 1 142 30 9132 2 142 26 9133 1 46 58 9134 2 45 30 9135 1 4659 9136 2 10 63 9137 1 58 58 9138 2 57 30 9139 1 58 59 9140 2 22 63 91411 70 58 9142 2 69 30 9143 1 70 59 9144 2 34 63 9145 1 10 64 9146 2 81 659147 1 84 60 9148 2 10 33 9149 1 22 64 9150 2 93 65 9151 1 96 60 9152 222 33 9153 1 34 64 9154 2 105 65 9155 1 108 60 9156 2 34 33 9157 1 83 329158 2 117 62 9159 1 119 57 9160 2 82 33 9161 1 95 32 9162 2 129 62 91631 131 57 9164 2 94 33 9165 1 107 32 9166 2 141 62 9167 1 143 57 9168 2106 33 9169 1 11 33 9170 2 119 58 9171 1 84 33 9172 2 12 60 9173 1 23 339174 2 131 58 9175 1 96 33 9176 2 24 60 9177 1 35 33 9178 2 143 58 91791 108 33 9180 2 36 60 9181 1 12 32 9182 2 119 28 9183 1 48 60 9184 2 12061 9185 1 24 32 9186 2 131 28 9187 1 60 60 9188 2 132 61 9189 1 36 329190 2 143 28 9191 1 72 60 9192 2 144 61 9193 1 120 32 9194 2 119 609195 1 48 26 9196 2 48 31 9197 1 132 32 9198 2 131 60 9199 1 60 26 92002 60 31 9201 1 144 32 9202 2 143 60 9203 1 72 26 9204 2 72 31 9205 1 8461 9206 2 11 64 9207 1 84 34 9208 2 12 67 9209 1 96 61 9210 2 23 64 92111 96 34 9212 2 24 67 9213 1 108 61 9214 2 35 64 9215 1 108 34 9216 2 3667

[0071] In another embodiment, the relative positions of the 9216 dots,in X and Y coordinates range from (0,0) to (64+VO, 144). In thisexemplary embodiment, the number of rows has increased by a verticaloffset (VO), where different compound placement zones have an equalnumber of rows, but include a different subset of the 64+VO rows. Forexample, FIGS. 3 illustrates four adjacent zones 330, 340, 350, and 360.The vertically offset zones allow the placement of alignment dots 320 onopposite sides of the ChemCard, efficient spacing between the dots 130,without requiring the size of the ChemCard to increase. In the exemplaryembodiment of FIG. 3, adjacent zones have the same number of rows (64),but they are offset by VO=5 rows. Thus, the rows in the second andfourth zones 340 and 360 are numbered from 1 to 64, while the rows inthe first and third zones are numbered from 6 to 69. One of skill in theart will recognize that the vertical offset in FIG. 3 (e.g. 5) isexemplary, and any vertical offset, e.g. V=1, 2, 3, 4, 6, 8, 10, 12, 15,20 may be implement according to the same concepts.

[0072] In one embodiment, the method of FIGS. 4 and 5 is executed usingsoftware running on a computer. One objective of the algorithm (fromwhich the software is based) is to determine a Sequence Array SA havingelements representative of dispense positions on a ChemCard, such thateach of the compounds placed in each of the dispenses satisfy theneighboring compound constraints, as discussed above. More specifically,the constraints for a particular compound are satisfied when eachoccurrence of a particular compound has different neighbors within theirrespective neighbor distances. Likewise, constraints for a particulardispense position are satisfied when each of the compounds in thedispense satisfy the constraints. For example, in an embodiment using a9,216 compound carrying ChemCard and a 12 pipette dispense mechanism(where all 12 pipettes are fired simultaneously), there are 768 possibledispense positions. In this case, A=768 and S_(A) contains non-repeatingvalues from 1 to 768 which represent dispense locations on the ChemCard.An array C of size A (C_(A)) contains, at each location A, a plurality Jof compounds to be dispensed at the dispense position stored in S_(A).Thus, in an embodiment that dispenses 2 occurrences of each compound,each compound will be in two different elements of C_(A). For example,C₁ may contain compounds 1-12 and C₂ may contain compounds 1-12, whileC₃ and C₄ each contain compounds 13-24. Thus, if S₁=324, S₂=531,C₁=compounds 1-12, and C₂=compounds 1-12 then compounds 1-12 will bedispensed at dispense positions 324 and 531. When the algorithm isdetermining the array S_(A), each of the 12 compounds in each of thedispenses S_(A) are tested against the constraints to determine if otheroccurrences of each of the compounds has the same neighbors. If any ofthe 12 compounds in the dispense violate the constraint check then thedispense position S_(A) violates the constraints and the value of S_(A)(representing a dispense position) must be changed in order to produce acomplete array S_(A) that satisfies the constraints.

[0073]FIG. 7 is a flow chart illustrating a method of determining anarray S_(A) such that each of the compounds in each of the A dispensepositions satisfy the neighbor constraints. In advantageous embodiments,each of the dispense positions dispenses a plurality J of compounds. Asdiscussed above, this may be accomplished by firing all of the pipettesin a dispense mechanism simultaneously (e.g., J=number of pipettes), or,alternatively, firing only a portion of the pipettes in a dispensemechanism over a particular location (e.g., J=number of pipettes firedover each ChemCard location). The plurality of dispense positions areprovided in an array P_(A), where a first element contains the X,Ycoordinates of the location of the dispense on the ChemCard and a secondelement contains a status indicator representative of whether eachparticular position P_(A) has been placed in the array S_(A). Thus, asan element of array S_(A) is filled with a dispense position P_(A), thestatus indicator of the particular dispense position in P_(A) is changedto indicate the position has been placed in the array S_(A). Forexample, if S₁ is filled with dispense position 425, the statusindicator of P₄₂₅ would be set to placed. In an advantageous embodiment,each of the status indicators for the dispense positions P are set tounplaced before the algorithm begins filling the array S_(A).

[0074] In block 610, the array S_(A) is filled with random, nonrepeating values from 1 to A. Thus, in an embodiment having 768 dispensepositions (i.e. A=768), the values of each S_(A) is a random valuebetween 1 and 768, where each of the values of different elements ofS_(A) are unique. For example, S₁=324, S₂=531, S₃=13, S₄=230. . .S₇₆₈=654, where each of the values of S_(A) represent dispense positionson a ChemCard (and corresponds with a dispense position P_(A)). Althougheach of the A elements of the array S_(A) are filled with dispensepositions, the corresponding status indicator P for the dispensepositions is not set to placed as the dispense positions in S_(A) atthis point are preliminary (e.g., constraint checks have not yet beenperformed). The status indicator for a particular dispense position P isset to placed only after the constraint checks (e.g., FIG. 8) have beensatisfied for the particular dispense position P.

[0075] In another embodiment, the array S_(A) may be initialized andfilled with any value. For example, each element of S_(A) may be set tozero (0).

[0076] In block 620 a counter X is set to zero. The counter X is used tostep through each element of the array S_(A), setting the value of eachS_(A) to a dispense position after each of the J compounds within eachof the dispense positions is checked against the neighbor constraints.In the 768 dispense position example, X will increment from 0 to 768,checking for constraint violations at each dispense position, beforecompleting the array S_(A). In alternative embodiments, the counter Xmay begin at any location within the array S_(A) and reset to zero afterchecking the last member of the array. For example, in a 768 dispenseposition system, X may be set to 300, iteratively incremented to 768after checking for constraint violations at each dispense position,reset to zero (0), and iteratively incremented to 298 after checking forconstraint violations at each dispense position. Alternatively, eachdispense position may be tested against the constraints in any otherorder, so long as each of the dispense positions (and more particularly,each of the compounds within a dispense) are tested against the neighborconstraints.

[0077] In block 630, counter X is incremented to the next dispenseposition to be tested. In the example of FIG. 7, each of the compoundsis placed on the ChemCard twice, in sequential dispenses (e.g., the sameJ compounds are dispensed at position S₁ and S₂). Thus, the constraintsonly need to be checked after each pair of compounds is assigned to aparticular dispense position. Thus, X is set to increment by 2 aftereach round of constraint checks. As will be discussed in more detailbelow, any number of each of the compounds may be placed on theChemCard, and, thus, X may be incremented by varying amounts.

[0078] In block 640, each of the J compounds in C_(X) is checked againstthe neighbor constraints (as described with reference to FIG. 8, forexample). For example, if the number of compounds in each dispense J=6then the constraints check is performed for each of the 6 compounds inthe dispense C_(X) at the dispense position in S_(X). In general, theneighbor constraint check determines whether a particular compound(e.g., at dispense location S_(X)) has different neighbors (within thedefined neighbor distance) than other occurrences of the particularcompound (e.g., at other dispense locations). One method of performing aneighbor constraint check is described in detail with reference to FIG.8. However, other methods of performing the neighbor constraint checkare contemplated.

[0079] Block 650 is a decision block that determines whether or notthere is a constraint violation for any of the J compounds in C_(X) atthe dispense position S_(X). As stated above, if any of the J compoundsin C_(X) violate the neighbor constraints at dispense position S_(X)then the value of S_(X) must be changed to another dispense position. Ifthere are no constraint violations for any of the compounds in C_(X)then the method continues to Block 690 where the status of the dispenseposition used in S_(X) is set to placed. However, if there areconstraint violations for any of the compounds in C_(X) then the methodcontinues to Blocks 670, and then to block 660 or 680 where adjustmentsto the position of at least the dispense position in S_(X) are made.

[0080] Block 670 is a decision block that determines if there areremaining unplaced dispense positions that have not been tested at thedispense location S_(X). In one embodiment, the status of the positionsP are polled in order to determined which dispense positions remainunplaced. As discussed above, in order to ensure that each compound inthe array satisfies the neighbor constraints, when a constraintviolation is found for any one of the J compounds C_(X) at a dispenseposition S_(X), the dispense position S_(X) is changed to anotheravailable dispense position and the constraint for each of the Jcompounds at the new dispense position S_(X) are tested. For example, ifS₂₃₂=342 and one of the J compounds in C₂₃₂ violates the neighborconstraints, S₂₃₂ may be changed to another dispense position. In oneembodiment, S_(X) is set to the value of the next dispense positionsthat has a status indicator set to unplaced. Thus, if the statusindicators in P₃₄₃ and P₃₄₄ have already been set to placed (e.g.,S₅₃=343 and S₂₁₁=344 and the neighbor constraints were satisfied for thecompounds C₅₃ at dispense position 343 and for the compounds C₂₁₁, atdispense position 344), but the status indicator for P₃₄₅ is set tounplaced, Block 680 will set the value of S_(X) to 345. However, ifthere are no remaining dispense positions that have not been testedagainst the neighbor constraints at the position of S_(X) (e.g., every Pwith a status indicator set to unplaced has already been tested atdispense position S_(X)), then the method continues to Block 660 wherethe value of X is decremented.

[0081] If Block 670 determines there are no remaining dispense positionsthat have not been tested against the neighbor constraints at theposition of S_(X), at Block 660 the value of X is decremented by 2. Asdiscussed above, the method of FIG. 7 is exemplary of a system thatplaces two occurrences of each compound on the ChemCard, and, thus, theconstraints only need be checked for every other element of the array.Thus, in a system that places 4 occurrences of each compound on a singleChemCard, the value of X may be decremented by 4, for example. After Xhas been decremented, the method returns to Block 670 to determine ifthere are remaining dispense positions that have not been tested at thedispense location S_(X). Note that the current value of S_(X) (e.g.,after S_(X) has been decremented in Block 660) will have satisfied theneighbor constraints in a previous iteration of the constraint checks ofBlock 640. However, because no acceptable dispense position could befound for the next array element S_(X+2), the value of S_(X) may bechanged in an attempt to adjust at least some of the neighbors ofS_(X+2) and allow S_(X+2) to pass the neighbor constraint test. Thus,the status indicator for the dispense position P that had already beenset to placed at position S_(X) is set to unplaced to ensure that theposition is available for another position in array S_(A). The methodthen returns to Block 640 where the constraints are checked for the newdispense position in S_(X) .

[0082] If Block 650 determines that there is no constraint violation forthe J compounds C_(X) at dispense position S_(X) then the methodcontinues to Block 690 where the status indicator for the dispenseposition tested in S_(X) is set to placed. For example, if S_(X)=562,then the status indicator of P₅₆₂ is set to placed. In one embodiment,the status indicator may be set to either a 1 or a 0, where 1 indicatesa placed dispense position and a 0 indicates an unplaced dispenseposition. In this embodiment, the array may be initialized with allzeros at the beginning of the method of FIG. 7. Likewise, when adispense position S_(X) satisfies the constraints, the status indicatorcorresponding with the dispense position of S_(X) may be changed to aone, indicating that the dispense position has been filled.

[0083] Block 695 is a decision block that determines whether each of thearray elements in S_(X) has been tested against the neighbor constraintsby determining if counter X is equal to A. For example, in a systemwhere the total dispense positions A=768, when X=766 at Block 695, thevalue of X will increment to 768 at Block 630 and the last element ofS_(A) will be checked against the constraints in Block 640. Afterdetermining that the constraints for the dispense position in S₇₆₈ aresatisfied, the array S_(A) is complete. Therefore, at Block 695 themethod determines that X=A (e.g., 768=768) and the method continues toBlock 699 which indicates that the array S_(A) is complete.

[0084]FIG. 8 is a flowchart illustrating one method of performing theneighbor constraint checks for an exemplary compound M. In oneembodiment, an algorithm searches for a pattern where one dot of eachcompound is at least a minimum distance (e.g., the neighbor distance)from every other compound in the array by checking the distance betweeneach pair of dots in the array. However, such an algorithm would performmany unnecessary calculations as constraints are checked with respect todots that are not within the neighbor distance D_(pmin) (and thereforedo not violate a constraint for the particular compound) of any of themultiple dots of a particular compound. Therefore, in an advantageousembodiment, rather than testing each occurrence of a particular dot withevery other dot in the array, only those dots within the neighbordistance D_(pmin) are checked.

[0085] As discussed above, for each dispense position a plurality of Jcompounds may be placed. Thus, for each dispense position, the flowchartof FIG. 8 may need to be executed for each of the plurality of Jcompounds before the neighbor constraints are satisfied for theparticular dispense position. The exemplary constraint check method ofFIG. 8 is specific to a system that places pairs of compounds in thearray. However, a similar method may easily be derived, based on thesame nearest neighbor principles, for a system that places any number ofdots of each compound in the array. The method of FIG. 8 makes referenceto M₁ and M₂, which are indicative of two occurrences of the compound M.As indicated above, the method of FIG. 8 may be implemented in the arraydevelopment method of FIG. 7, as well as any other method that requiresa neighbor constraint check.

[0086] In order to provide a graphic example of the operation of theneighbor constraint check of FIG. 8, FIG. 9 will now be described andreferred to with reference to the constraint check method of FIG. 8.FIG. 9 illustrates a portion of a placement array geographicallyarranged as the compounds would be placed on a ChemCard. The exemplaryembodiment of FIG. 9 utilizes a honeycomb placement pattern. Thecompound M, including M₁ and M₂, represents a dot for which constraintsare being checked, wherein M₁ is to be dispensed in a first dispense(e.g., for a particular dispense T, M₁ is one of the compounds J inC_(T) that will be dispensed at location S_(T)) and M₂ is to bedispensed in a second dispense (e.g., M₂ is one of the compounds J inC_(T+)that will be dispensed at location S_(T+1)). The pairs of dotslabeled Q₁- Q₆ represent the pairs of neighbors of M₂ at the currentlocation within the array S. Each of the unlabeled dots (representativeof dot placement locations) may have a compound already assigned tothem, or, alternatively, may be positions that have not been assignedcompounds yet.

[0087] In Block 702 the variable D is set to equal the distance betweenM₁ and M₂. In an embodiment that places multiple compounds in eachdispense position (e.g., J>1), so long as the relative positions of eachof the compounds in the dispense mechanism remains constant, D willremain constant for each of the compounds in the dispense.

[0088] In Block 704 the variable D is compared to the neighbor distanceD_(pmin). If the distance D is less than D_(pmin) there is a constraintviolation and the method ends. More particularly, if D is less thanD_(pmin) then both occurrence of M (i.e. M₁ and M₂) are close enough toone another so that an active spot pattern diffusing from compound M maynot be definitively attributable to the compound M. This may occur as aresult of the diffusion spots from M₁ and M₂ overlapping so that a spotdetection machine recognizes only a single spot pattern. If the distanceD is not less than D_(pmin) there is no constraint violation and themethod continues to Block 710.

[0089] In Block 710, the method determines the neighbors of theoccurrence of M at the current dispense position (designated as M₂).Thus, when used as part of Block 640 (FIG. 7), Block 710 determines theneighbors of the compound M₂ at dispense position S_(X) (where compoundM₁ is placed at dispense position S_(X−1)). In the example of FIG. 9,the neighbors are those compounds within the radius of the circle 940having a radius of D_(pmin), where the line 905 is set to the distanceD_(pmin). The neighbors of compound M₂ are referred to herein as Q,wherein Q includes each neighbor Q₁, Q₂, Q₃. . . Q_(Y), where Y is thetotal number of neighbors of M₂. The number of dots in a neighborhood,called the size of the neighborhood, depends on the value of D_(pmin),the dot grid spacing, and the location of the central dot (e.g., edgedots have smaller sets). A neighborhood's size is always much smallerthan the total number of dots on a card. Thus, in the example of FIG. 9,the neighbors of M₂ include Q₁- Q₆. In other embodiments, the number ofneighbors of compound M may vary greatly depending on the particularassay process and the method of determining the neighbors.

[0090] In Block 720 the variable Y is initialized to the value of zero.The variable Y is incremented as neighbor constraints are checked foreach neighbor Q_(Y) of M₂.

[0091] In Block 730 the variable Y is incremented by 1 to move theconstraint check to the next neighbor. For example, if the method hadjust completed checking the neighbor constraints with respect to M andQ₃ then Y is incremented in Block 730 so that the neighbor constraintsmay now be checked with respect to M and Q₄.

[0092] In Block 770 the variable D is set equal to the distance betweenMl and the occurrence of compound Q_(Y) that is not a neighbor to M₂.With reference to exemplary FIG. 9, D is illustrated by the line 930 forthe situation where Y=3 (i.e. constraint are being checked for M withrespect to neighbor Q₃).

[0093] Block 780 is a decisions block that determines whether thedistance D between M₁ and the occurrence of compound Q_(Y) that is not aneighbor to M₂ is greater than the neighbor distance D_(pmin). Asdescribed above, the neighbor distance D_(pmin) may be determined basedon many factors. If the distance D is greater than the neighbor distanceD_(pmin), the constraints for compound M have been met and the methodcontinues to Block 790. However, if the distance D is less than D_(pmin)the method continues to Block 799 indicating a constraint violation.

[0094] By halting the process as soon as the constraint is violated, themethod rejects not only the current sub-pattern, but all patterns ofwhich it is a part. For example, consider an array where the first 49dispense positions have satisfied the constraints S_(A) (1 to 49) andthen the algorithm discovers that dispense position 50 violates theconstraint check. Thus, all patterns that start with this sub-pattern of50 dispense positions, S_(A) (1 to 50), would violate the constraint.This set of all patterns having the same sub-pattern consists of(768-50)?=718! patterns. Therefore, with the discovery of one constraintviolation a large number of unsuitable patterns can be eliminated fromconsideration.

[0095] If the method determines that a particular neighbor Q_(Y)satisfies the neighbor constraint check in block 780 the methodcontinues to Block 790. In decision Block 790, if the variable Y isequal to the number of compounds in the neighborhood of M₂ the methodcontinues to Block 795 and an indication that no constraint violationsfor compound M at the dispense position S_(X) is returned. However, if Yis less than the number of neighbors in the neighborhood of M₂, themethod returns to block 730 where Y is incremented and the neighborconstraints are checked for another neighbor of M₂.

[0096] Specific parts, shapes, materials, functions and modules havebeen set forth, herein. However, a skilled technologist will realizethat there are many ways to fabricate the system of the presentinvention, and that there are many parts, components, modules orfunctions that may be substituted for those listed above. While theabove detailed description has shown, described, and pointed out thefundamental novel features of the invention as applied to variousembodiments, it will be understood that various omissions andsubstitutions and changes in the form and details of the componentsillustrated may be made by those skilled in the art, without departingfrom the spirit or essential characteristics of the invention.

What is claimed is:
 1. An array of n unique materials, each of whichappears in the array at least two times and which has a plurality ofneighboring materials, wherein for each of the n materials in the array,the neighboring materials in one occurrence of the material aredifferent from the neighboring materials of all other occurrences of thematerial, wherein n is greater than 25:
 2. The array of claim 1 whereinsaid materials are considered neighboring materials of a particularmaterial if they are within a predetermined radius around saidparticular material.
 3. The array of claim 2 wherein said predeterminedradius is in the range of about 1 mm to 1 cm.
 4. The array of claim 2wherein said predetermined radius is about 3 mm.
 5. The array of claim 1wherein said materials are considered neighboring materials of aparticular material if they are within a predetermined dot-pitchdistance from said particular material.
 6. The array of claim 4, whereinsaid predetermined dot-pitch distance is 1 dot pitch.
 7. The array ofclaim 4, wherein said predetermined dot-pitch distance is between 1 and5 dot pitch distances.
 8. The array of claim 4, wherein saidpredetermined dot-pitch distance is greater than 5 dot pitch distances.9. The array of claim 1, wherein n is greater than
 300. 10. The array ofclaim 1, wherein n is greater than
 4000. 11. The array of claim 1,wherein n is greater than
 9000. 12. The array of claim 1, further incombination with a planar porous assay matrix, such that a surface ofthe porous assay matrix is in contact with each of the n materials ofthe array in such a manner that the materials can diffuse into theporous assay matrix.
 13. The array of claim 12 further comprising asubstantially non porous assay matrix in contact with said porous assaymatrix and containing at least one assay reagent capable of interactingwith any of the materials on the porous assay matrix.
 14. The array ofclaim 12, in which the porous assay matrix contains at least one assayreagent capable of interacting with any of the materials in the arraythat is active in a test assay, wherein the test assay displays positiveresults (if any) within a time period t, during which time t thematerials diffuse within the porous assay matrix to form a spot ofdiameter d, and wherein “neighboring materials” are within apredetermined distance of the center of the spot.
 15. The array of claim12 further comprising a second porous assay matrix in contact with saidporous assay matrix and containing at least one assay reagent capable ofinteracting with any of the materials in the array that is active in atest assay, wherein the test assay displays positive results (if any)within a time period t, during which time t the materials diffuse withinthe porous assay matrix and the second porous assay matrix to form aspot of diameter d on the second porous assay matrix and wherein“neighboring materials” are within a predetermined distance of thecenter of the spot.
 16. The array of claim 12, wherein “neighboringmaterials” include materials within a radius of about 3.5 mm.
 17. Amethod of testing a plurality of samples of different substances fortheir ability to enhance or inhibit a biological process, the methodcomprising: providing an array of at least two dots of each of saidsamples on a planar matrix such that each of said at least two dots iscentered at its own distinct site, wherein at least one of said at leasttwo dots of each of said samples is at least a predetermined distancefrom at least one of said dots of each of said plurality of samples;transferring the array from the planar matrix into a uniformly dispersedassay reagent; and observing the interaction of each of said substanceswith said assay reagent and correlating said interaction with an abilityof each of said substances to enhance or inhibit said biologicalprocess.
 18. The method of claim 17, further comprising: providing asecond array of at least two dots of each of said samples on a secondplanar matrix such that each of said at least two dots is centered atits own distinct site, wherein at least one of said at least two dots ofeach of said samples is at least a predetermined distance from at leastone of said dots of each of said plurality of samples, and a pattern ofplacement of said dots on said second array is different than a patternof placement of said dots on said first array; placing said uniformlydispersed assay reagent on said second planar matrix; and observing theinteraction of each of said substances with said assay reagent andcorrelating said interaction with an ability of each of said substancesto enhance or inhibit said biological process.
 19. The method of claim17, further comprising placing a second uniformly dispersed assayreagent on said uniformly dispersed assay reagent, observing a secondinteraction of each of said substances with said second uniformlydispersed assay reagent, and correlating said second interaction with anability of each of said substances to enhance or inhibit said biologicalprocess.
 20. The method of claim 19, further comprising placing a thirduniformly dispersed assay reagent on said second uniformly dispersedassay reagent, observing a third interaction of each of said substanceswith said third uniformly dispersed assay reagent, and correlating saidthird interaction with an ability of each of said substances to enhanceor inhibit said biological process.
 21. The method of claim 17, whereinsaid planar matrix comprises a plurality of alignment dots configured todiffuse into said uniformly dispersed assay reagent; said alignment dotson said uniformly dispersed assay reagent providing reference points foraligning said uniformly dispersed assay reagent with said planar matrixso that each particular interaction is correlated with each particularsubstance from which each interaction resulted.
 22. The method of claim20, wherein said planar matrix comprises a plurality of alignment dotsconfigured to diffuse into said uniformly dispersed assay reagent, saidsecond uniformly dispersed assay reagent, and said third uniformlydispersed assay reagent; said alignment dots on said third uniformlydispersed assay reagent providing reference points for aligning saidthird uniformly dispersed assay reagent with said planar matrix so thateach particular third interaction is correlated with each particularsubstance from which each third interaction resulted.
 23. A method oftesting a plurality of samples of different substances for their abilityto enhance or inhibit a biological process, the method comprising:depositing in an array at least one dot of each of said samples onto aplurality of planar matrixes such that each of said at least one dot iscentered at its own distinct site, wherein at least one of said dots ofeach of said samples is at least a predetermined distance from at leastone of said dots of each of said plurality of samples; transferring thearray of samples from the plurality of planar matrixes into a uniformlydispersed assay reagent; and observing the interaction of each of saidsubstances with said assay reagent and correlating said interaction withan ability of each of said substances to enhance or inhibit saidbiological process.
 24. A system for creating an array of samplecompounds comprising: a relatively flat carrier configured to support aplurality of samples; and a dispensing mechanism configured to dispenseat least two dots of each of said plurality of samples of differentcompounds on said flat carrier such that each of said at least two dotsof each of said plurality of samples has a different set of neighboringcompounds within a predetermined distance.
 25. The system of claim 24,wherein said samples are chemically bonded to said relatively flatcarrier.
 26. The system of claim 24, wherein said samples are free todiffuse from said relatively flat carrier.
 27. The system of claim 24,wherein said dispensing mechanism simultaneously dispenses a portion ofsaid plurality of samples in a first relative orientation on at leasttwo locations on said flat container.
 28. The system of claim 27,wherein none of said samples in said portion of said plurality ofsamples are neighboring compounds.
 29. The system of claim 27, whereinsaid portion of said plurality of samples comprises twelve samples. 30.The system of claim 24, wherein said flat carrier comprises a pluralityof alignment dots configured to diffuse into a material brought intocontact with the flat carrier and provide reference points for aligningsaid material brought into contact with the flat carrier with said flatcarrier so that each particular diffused dot is correlated with eachparticular dot on said flat carrier from which said diffused dotresulted.
 31. An array of samples in which each sample appears at leasttwice and there are at least 768 dispenses of groups of 12 samples. 32.An array of samples in which each sample appears at least twice andthere are at least 4608 samples, wherein the array comprises 144 columnsand 64 rows and the samples are arranged substantially according to therelative coordinates shown in Table
 1. 33. A method for performing anassay, comprising: providing a substantially planar substrate having anarray of at least two dots of each of a plurality of test materials,wherein each of said dots has a plurality of neighboring test materialsand is placed such that the neighboring materials in one occurrence ofthe material are different from the neighboring materials of all otheroccurrences of the material; and transferring the array of testmaterials into a uniformly-dispersed assay reagent that participates inindicating which of the test materials are active in the assay whilemaintaining the relative positioning of the test materials vis-a-viseach other.
 34. The method of claim 33, wherein transferring the arrayof test materials comprises contacting the array with the assay reagentand allowing the materials to diffuse into the assay reagent.
 35. Themethod of claim 33, wherein transferring the array of test materialscomprises contacting the array with a non-porous surface carrying saiduniformly dispersed assay reagent and allowing the materials to havesurface reactions with said assay reagent.
 36. The method of claim 33,wherein transferring the array comprises transferring the materials intoa first matrix, and then contacting the first matrix with the assayreagent.
 37. The method of claim 33, wherein transferring the arraycomprises contacting the array with a gel into which the materials candiffuse.
 38. The method of claim 33, wherein the uniformly-dispersedassay reagent is surface bound on a non-porous surface so thattransferring the array comprises contacting the array with saidnon-porous surface.
 39. An algorithm for formulating an array S having Aelements (S_(A)), wherein the value of each element S_(A) represents adispense position on a card, wherein a dispensing mechanism dispenses aplurality of compounds at each dispense position, the algorithmcomprising: (a) setting each of the A elements of the array S to arandom, non-repeating value from 1- A, wherein each S_(A) is set to apreliminary dispense position; (b) providing an array C having Aelements (C_(A)), wherein each of said A elements of the array Ccomprises J representations of compounds; (c) setting a counter x tozero; (d) incrementing x by 2; (e) determining whether each of said Jcompounds in C_(X) satisfy a placement constraint with respect tocertain other compounds in the array C; (f) if step (e) determines thatthere in a constraint violation with one or more of said J compounds inC_(x); (1) decrementing x by 2; (2) determining if there are remainingdispense positions that have not been tested in S_(X) against theconstraints of step (e); (3) if step (2) determines that there are noremaining dispense positions that have not been tested in S_(X) againstthe constraints of step (e), repeating steps (1) and (2); (4) changingthe value of S_(X) to a remaining dispense position that has not beentested in S_(X) against the constraints of step (e); (5) return to step(e); (g) if step (e) determines that there is not a constraint violationwith any of said J compounds in C_(X), return to step (d).
 40. The arrayof claim 39, wherein C_(x) and C_(x+1) are equal and wherein x=any oddinteger<A.
 41. A method for creating an array of a plurality ofmaterials, each material occurring at least twice within the array andhaving different neighboring materials in each occurrence, the methodcomprising: (a) creating a candidate arrangement of materials containingpairs of n said materials in a spatial relationship; (b) testing whethera first occurrence and a second occurrence of each of said materialshave different neighbors; (c) if the criteria of (b) is not satisfied,changing said spatial relationship of at least some of n said materials;and (d) repeating steps (b) and (c) until the criteria of (b) issatisfied.
 42. The method of claim 41, wherein said candidatearrangement created in step (a) comprises each of said plurality ofmaterials such that when the criteria of (b) is satisfied, the array iscomplete.
 43. The method of claim 41, wherein said candidate arrangementcreated in step (a) comprises a portion of said plurality of materials,the method further comprising: (e) expanding said candidate arrangementof materials by increasing n by a predetermined number; (f) repeatingsteps (b)-(e) until a final candidate arrangement is created containingeach of said plurality of materials.
 44. The method of claim 43, whereinsaid changing said spatial relationship of at least some of n saidmaterials comprises: determining whether a placement of a nth materialin every open location within said candidate arrangement fails tosatisfy the criteria of (b); decrementing n if said nth material failsto satisfy the criteria of (b) in every open location within saidcandidate arrangement; and changing said spatial relationship of atleast some of n said materials.
 45. A method for formulating an array Shaving A elements (S_(A)), wherein the value of each element of S_(A)represents a dispense position for one or more materials on a substrate,wherein each material occurs at least two times (C₁ and C₂) in S_(A),with the constraint that when the distance from one of C₁ and C₂ to anyoccurrence of any other material is less than or equal to a minimumvalue D, then the distance from the other of C₁ and C₂ to any occurrenceof such other material is greater than D, comprising: tentativelyassigning a plurality of elements to S_(A); for each first occurrence ofa material, determining a set of Q materials that are within a distanceof D; for each second occurrence of a material, ascertaining whethereach of the Q materials are within a distance of D and, if so, changingthe location of at least one material.
 46. A method for formulating anarray containing pairs of materials, wherein each member of the pair hasdifferent neighboring materials than the other member of the pair,comprising: (a) tentatively assigning a plurality of materials to arraylocations; (b) testing to ascertain whether a first member of a pair hasdifferent neighboring materials than a second member of a pair, and ifnot, then (c) sequentially repeating step (a) with at least one alteredmaterial location and repeating step (b), until each member of each pairhas different neighboring materials.
 47. The method of claim 46, whereinthe testing step comprises measuring the distance from the first memberof the pair to the tentative array locations of some or all of the othermaterials in the array, measuring the distance from the second member ofthe pair to the tentative array locations of some or all of the othermaterials in the array, and performing a comparison of data resultingfrom the measurements.
 48. The method of claim 47, wherein the dataresulting from the measurements comprises a first set of materialslocated within a predetermined distance of the first member of the pair.49. The method of claim 48, wherein the data resulting from themeasurements further comprises a second set of materials located withina predetermined distance of the first member.
 50. A method of creatingan array of sample compounds comprising: providing a relatively flatcarrier configured to support a plurality of samples; and dispensing atleast two dots of each of said plurality of samples of differentcompounds on said flat carrier such that each of said at least two dotsof each of said plurality of samples has a different set of neighboringcompounds within a predetermined distance.